In a camp there were stored food of 48 soldiers for 7 weeks. If 8 nore soldiers join the camp lets find for how many weeks it will be sifficient with the same food?​

To find the area of the triangle with side lengths 5, 12, and 14 inches and an angle measuring 20°, Howard constructs an altitude to the 14-inch side.

The area of the triangle can be calculated using the formula: Area = (1/2) * base * height.

To find the area of the triangle, Howard needs to determine the length of the altitude drawn to the 14-inch side. This altitude will form a right triangle with a 14-inch side.

Using trigonometric functions, Howard can find the length of the altitude. Since he knows the length of the side opposite the 20° angle (5 inches) and the length of the hypotenuse (14 inches), he can use the sine function. The sine of an angle is equal to the ratio of the side opposite the angle to the hypotenuse. Thus, sin(20°) = opposite / hypotenuse. Rearranging the equation, we find that the length of the altitude is given by altitude = sin(20°) * 14 inches.

Once Howard has the length of the altitude, he can calculate the area of the triangle using the formula: Area = (1/2) * base * height. The base of the triangle is 12 inches (the side adjacent to the altitude), and the height is the length of the altitude.

By plugging in the values, Howard can calculate the area of the triangle.

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Currently, the Earth is facing a sixth mass extinction event, which is primarily caused by human activity, including habitat destruction, overhunting, and climate change.

The Earth has undergone several mass extinction events over the last 4.6 billion years. The precise number of mass extinctions is still under discussion, and estimates vary.

There have been five major mass extinction events in the last 4.6 billion years of Earth's history. The first mass extinction event occurred during the Ordovician period (443 million years ago), and the most recent occurred at the end of the Cretaceous period (66 million years ago).

It is believed that these mass extinction events were caused by natural phenomena such as volcanic eruptions, asteroid impacts, and climate change, as well as human activities like deforestation and pollution.The most well-known mass extinction event was the one that wiped out the dinosaurs at the end of the Cretaceous period.

However, mass extinction events are not just ancient history.

Currently, the Earth is facing a sixth mass extinction event, which is primarily caused by human activity, including habitat destruction, overhunting, and climate change.

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(a) X follows a binomial distribution with n = 12 and p = 1/6; P(X < 4) = 0.873. (b) X follows a geometric distribution with p = 1/6; P(X > 12) = (5/6)^12 ≈ 0.0326, meaning the event of not rolling a six in the first 12 throws.

(a) The distribution of X is a binomial distribution with parameters n = 12 (number of trials) and p = 1/6 (probability of success on each trial, i.e., rolling a six). We can compute P(X < 4) as follows:

P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

= (5/6)^12 + 12(1/6)(5/6)^11 + 66(1/6)^2(5/6)^10 + 220(1/6)^3(5/6)^9

≈ 0.918

(b) The distribution of X is a geometric distribution with parameter p = 1/6 (probability of success, i.e., rolling a six on each trial). We can compute P(X > 12) as follows:

P(X > 12) = (5/6)^12

≈ 0.032

This event describes the probability that it takes more than 12 rolls to get the first six. In other words, after rolling the die 12 times, you still have not rolled a six.

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Given the inequality problem,The sum of a number and 15 is no greater than 32. We need to solve the inequality problem and select all possible values for the number.

So, we can write it mathematically as:x + 15 ≤ 32 Subtract 15 from both sides of the equation,x ≤ 32 - 15x ≤ 17 Therefore, all possible values for the number is x ≤ 17.The solution of the given inequality problem is x ≤ 17.Answer: The possible values for the number is x ≤ 17.

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Answer:

a) 4(3) - 2(5) = 12 - 10 = 2

b) 2(3^2) + 3(5^2) = 2(9) + 3(25)

= 18 + 75 = 93

In the given problem, the independent variable is t and the dependent variable is d. The relationship between the two variables can be described by the following formula: d = 5t + 7. When t = 2, we can find the corresponding value of d by substituting t = 2 in the formula: d = 5(2) + 7 = 17.

Therefore, when t = 2, the value of d is 17. Here is the detailed explanation of independent and dependent variables: The independent variable is the variable that is being changed or manipulated in an experiment. In other words, it is the variable that is presumed to be the cause of the change in the dependent variable.

It is usually plotted on the x-axis of a graph. The dependent variable is the variable that is being observed or measured in an experiment. It is presumed to be the effect of the independent variable.

It is usually plotted on the y-axis of a graph. In the given problem, t is the independent variable because it is being varied or manipulated, and d is the dependent variable because it is being observed or measured and its value depends on the value of t.

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Without information about the standard deviation or the sample standard deviation, it is not possible to determine the greatest amount by which the estimated mean time could differ from the true mean with a probability of 0.95.

To determine the greatest amount by which the estimated mean time could differ from the true mean with a probability of 0.95, we can use the concept of the margin of error in confidence intervals.

The margin of error is a measure of the uncertainty associated with an estimated parameter, such as the mean, based on a sample. It represents the maximum amount by which the estimate could differ from the true population parameter.

In this case, we can use the standard formula for the margin of error for estimating the population mean:

Margin of Error = Z * (Standard Deviation / √(Sample Size))

The Z value corresponds to the desired level of confidence. For a 95% confidence level, Z is approximately 1.96.

However, to calculate the margin of error, we need to know the standard deviation of the population or an estimate of it. If the standard deviation is not known, we can use the sample standard deviation as an estimate, assuming that the sample is representative of the population.

Once we have the sample standard deviation, we can substitute the values into the formula to calculate the margin of error.

It's important to note that the margin of error gives a range within which we can be confident that the true population mean lies. It does not provide a specific point estimate of the difference between the estimated mean and the true mean.

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The integral is (x^2 + 4x)sin(x) - (2x + 4)cos(x) + 2sin(x) + C.

The integral is:

∫(x^2 + 4x)cos(x)dx

Using integration by parts, we can set u = x^2 + 4x and dv = cos(x)dx, which gives us du = (2x + 4)dx and v = sin(x). Then, we have:

∫(x^2 + 4x)cos(x)dx = (x^2 + 4x)sin(x) - ∫(2x + 4)sin(x)dx

Applying integration by parts again, we set u = 2x + 4 and dv = sin(x)dx, which gives us du = 2dx and v = -cos(x). Then, we have:

∫(x^2 + 4x)cos(x)dx = (x^2 + 4x)sin(x) - (2x + 4)cos(x) + 2∫cos(x)dx + C

= (x^2 + 4x)sin(x) - (2x + 4)cos(x) + 2sin(x) + C

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The average rate of change of f over the given interval can be found to be 34.

The average rate of change of a function f(x) over an interval [a, b] is given by the formula:

( f ( b ) - f ( a ) ) / (b - a)

The function given is f(x) = x³ - 9x. So, to find the average rate of change over the interval [1, 6] :

f(1) = (1)³ - 9(1) = 1 - 9 = -8

f(6) = (6)³ - 9(6) = 216 - 54 = 162

So, the average rate of change is:

= (f ( 6 ) - f ( 1 )) / (6 - 1)

= (162 - (-8)) / 5

= 170 / 5

= 34

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The series converges absolutely. The ratio test states that if the limit as n approaches infinity of the absolute value of the ratio of the (n+1)th term to the nth term is less than 1, then the series converges absolutely.

If the limit is greater than 1, the series diverges. If the limit is equal to 1, then the test is inconclusive and another test must be used. For the given series 3n/(2n)!, the ratio of successive terms is (3(n+1)/(2(n+1))!) / (3n/(2n)!) = 3(n+1)/(2n+2)(2n+1). Simplifying this gives the ratio as 3/((2n+2)/(n+1)(2n+1)).

Taking the limit as n approaches infinity, we get that the ratio approaches 0. Therefore, the series converges absolutely.

When n=7, the ratio of successive terms is 30/1176, or 5/196.

Taking the limit of this ratio as n approaches infinity, we get that it approaches 0. Therefore, the series converges absolutely.

By the ratio test, we have determined that the series 3n/(2n)! converges.

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To determine the second factor that will result in 20x+10y when the two factors are multiplied, we will have to find the greatest common factor (GCF) of the two numbers, then divide each term by that GCF.

Then, we will write the result as a product of two factors. To find the GCF of 20x and 10y, we will have to find the greatest number that divides both 20x and 10y evenly. We can start by factoring out the greatest common factor of the coefficients 20 and 10 which is 10.10(2x + y)We see that 2x + y is the second factor that will result in 20x+10y when the two factors are multiplied. This is because, when we multiply the two factors together, we get:[tex]10(2x + y) = 20x + 10y[/tex] So, the second factor that will result in 20x+10y when the two factors are multiplied is 2x + y.

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The broker may be held liable for violating the Fair Housing Act if it is proven that they intentionally engaged in discriminatory practices based on race or any other protected characteristic.

Step 1: The salesperson scheduled showings for Couple A in a predominantly Caucasian neighborhood and Couple B in a more diverse neighborhood.

Step 2: It was discovered that the couples were HUD testers, and a discrimination complaint was filed.

Step 3: Under the Federal Fair Housing Act, the broker may be held liable for violating the law if it is proven that they intentionally engaged in discriminatory practices based on race or any other protected characteristic.

Step 4: The Fair Housing Act prohibits discrimination in housing based on race, color, religion, sex, national origin, disability, or familial status.

Step 5: If it can be demonstrated that the broker treated Couple A and Couple B differently based on their race or any other protected characteristic, they may be found in violation of the Fair Housing Act.

Therefore, the outcome of the case would depend on the evidence presented and whether it can be proven that the broker intentionally engaged in discriminatory practices. If found guilty, the broker may face legal consequences, such as fines or other penalties, for violating the Fair Housing Act.

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The expected value of Y is μ(σ - 1) and the variance of Y is σ⁴.

To find the expected value and variance of Y = σX - μ, where X is a random variable with expected value μ and variance σ², we'll use the following properties:

1. E(aX + b) = aE(X) + b, where a and b are constants.
2. Var(aX + b) = a²Var(X), where a is a constant.

Step 1: Find the expected value of Y.

E(Y) = E(σX - μ) = σE(X) - E(μ)
Since E(X) = μ,
E(Y) = σμ - μ = μ(σ - 1).

Step 2: Find the variance of Y.
Var(Y) = Var(σX - μ) = σ²Var(X)
Since Var(X) = σ²,
Var(Y) = σ²(σ²) = σ⁴.

So, the expected value of Y is μ(σ - 1) and the variance of Y is σ⁴.

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The number more of Michael's friends that like pizza compared to his neighbors are 2 more of his friends.

First, let's calculate how many of Michael's friends and neighbors like pizza:

55% of his 40 friends like pizza, so the number of his friends who like pizza is:

=  55 / 100 x 40

= 22

80% of his 25 neighbors like pizza, so the number of his neighbors who like pizza is :

= 80 / 100 x 25

= 20

Therefore, 2 more of Michael's friends like pizza compared to his neighbors.

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After considering the given data we come to the conclusion that the vertex for the given quadratic equation is  (-1,-4).

Here, the vertex form of a quadratic function is represented by f (x) = a(x - h)² + k,
Here
(h, k) = vertex of the parabola .
The given quadratic function p(x) = (x - 1)(x + 3) could be expanded to p(x) = x² + 2x - 3. Now comparing this with the vertex form of a quadratic function, we can understand that the vertex is (-1, -4) .

Hence, the vertex of p(x) = (x - 1)(x + 3) is (-1,-4).
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The complete question is
A quadratic function is defined by p (x)= (x - 1) ( x +  3) .What is the vertex of p (x) ?

Charlie starts with $984.20 in his savings account and uses $381.80 to buy his plane ticket. This leaves him with:

$984.20 - $381.80 = $602.40

Next, Charlie transfers 1/4 of his remaining savings into his checking account. To do this, he needs to find 1/4 of $602.40:

(1/4) x $602.40 = $150.60

Charlie transfers $150.60 from his savings account to his checking account, leaving him with:

$602.40 - $150.60 = $451.80

Therefore, Charlie has $451.80 left in his savings account after buying his plane ticket and transferring 1/4 of his remaining savings to his checking account.

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The equilibrium quantity is 625.

The producer surplus at the equilibrium quantity is 234,125.

To find the equilibrium quantity, we need to find the value of x where demand equals supply.

Equating demand and supply:

d(x) = s(x)

500 - 0.2x = 0.6x

Simplifying and solving for x:

0.8x = 500

x = 625

To find the producer surplus at the equilibrium quantity, we first need to find the equilibrium price, which is the price at which the quantity demanded equals the quantity supplied.

Substituting x = 625 into either the demand or supply function, we get:

d(625) = 500 - 0.2(625) = 375

s(625) = 0.6(625) = 375

Therefore, the equilibrium price is 375.

The producer surplus at the equilibrium quantity is the area above the supply curve and below the equilibrium price. To find this area, we need to find the total revenue received by the producers and subtract their total variable costs.

Total revenue at the equilibrium quantity is:

TR = P x Q = 375 x 625 = 234,375

Total variable costs at the equilibrium quantity are:

TVC = 0.4 x Q = 0.4 x 625 = 250

Therefore, the producer surplus at the equilibrium quantity is:

PS = TR - TVC = 234,375 - 250 = 234,125

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To find the equilibrium quantity, we need to set the demand function equal to the supply function and solve for x:

500 - 0.2x = 0.6x

Combining like terms, we get:

500 = 0.8x

Dividing both sides by 0.8, we find:

x = 500 / 0.8 = 625

So the equilibrium quantity is 625.

To find the producer's surplus at the equilibrium quantity, we need to calculate the area between the supply curve and the market price.

The market price is determined by the demand and supply equations when they are equal. Plugging in the equilibrium quantity of x = 625 into either the demand or supply function will give us the market price.

Using the supply function, we have:

s(x) = 0.6x

s(625) = 0.6 * 625 = 375

So the market price is 375.

The producer's surplus is the area between the supply curve and the market price, up to the equilibrium quantity.

To calculate the producer's surplus, we can integrate the supply function from 0 to the equilibrium quantity of x = 625:

Producer's Surplus = ∫[0, 625] s(x) dx

= ∫[0, 625] 0.6x dx

= 0.6 * ∫[0, 625] x dx

= 0.6 * [(1/2) x²] |[0, 625]

= 0.6 * (1/2) * (625)²

= 0.6 * (1/2) * 390625

= 117187.5

So the producer's surplus at the equilibrium quantity is 117187.5 units.

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a. The decay of 232Th to 236U through emission of a 1z = 90 2s particle is not possible.

b. The decay of 238Pu to 236U through emission of a 1z = 94 2s particle is possible.

c. The decay of 11B to 11B through emission of a 1z = 52 1s particle is not possible.

d. The decay of 33P to 32S through emission of a 1z = 152 1s particle is not possible.

e. No information is provided for decay e.

a. The decay of 232Th to 236U through emission of a 1z = 90 2s particle is not possible. This is because the atomic number of the daughter nucleus (236U) would be 92 (the same as uranium), and the mass number would be 238. Therefore, this decay violates the law of conservation of element.

b. The decay of 238Pu to 236U through emission of a 1z = 94 2s particle is possible. This is because the atomic number of the daughter nucleus (236U) would be 92 (uranium), and the mass number would be 234. Therefore, this decay is possible.

c. The decay of 11B to 11B through emission of a 1z = 52 1s particle is not possible. This is because the atomic number of the daughter nucleus (11B) would be the same as that of the parent nucleus, and the mass number would also remain the same. Therefore, this decay violates the law of conservation of mass and charge.

d. The decay of 33P to 32S through emission of a 1z = 152 1s particle is not possible. This is because the atomic number of the daughter nucleus (32S) would be less than that of the parent nucleus (33P). Therefore, this decay violates the law of conservation of charge.

e. No information is provided for decay e.

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True. If a matrix has at least one row that is all zeroes, it means that the corresponding equation in the system of linear equations will be of the form 0x = 0, which is always true for any value of x.

Therefore, this equation will not impose any restrictions on the values of the variables, and hence, there will be at least one free variable.

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Probabilities for the standard normal distribution z. a. p(0 - 1.25) = P(Z < -1.25) = 0.1056.

Using a standard normal distribution table or a calculator, we can find:

P(0 - 1.25 < Z < 0) = P(Z < 0) - P(Z < -1.25) = 0.5 - 0.1056 = 0.3944

where Z is a standard normal random variable with mean 0 and standard deviation 1.

Therefore, p(0 - 1.25) = P(Z < -1.25) = 0.1056.

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The probability of the complement of A is 1 - P(A) = 1 - 0.25 = 0.75.
The answer is C. 0.75.

The probability of an event, like rolling an even number, is the number of outcomes that constitute the event divided by the total number of possible outcomes. We call the outcomes in an event "favorable outcomes".

Given that P(A) = 0.25, the probability of the complement of A is:
P(A') = 1 - P(A)
The complement of event A is all the outcomes that are not in event A. The probability of an event and its complement always add up to 1.
To find the probability of the complement of A, we can simply subtract P(A) from 1:
P(A') = 1 - 0.25 = 0.75
So, the correct answer is C. 0.75.

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The volume of the quadrilateral prism is 525 cm³.

To find the volume of a regular quadrilateral prism, we need to use the given information about the perimeter of the base and the area of one of the lateral faces.

First, let's focus on the perimeter of the base. Since the base of the prism is a regular quadrilateral, it has four equal sides. Let's denote the length of each side of the base as "s". Therefore, the perimeter of the base is given as 4s = 60 cm.

Dividing both sides by 4, we find that each side of the base, s, is equal to 15 cm.

Next, let's consider the area of one of the lateral faces. Since the base is a regular quadrilateral, each lateral face is a rectangle with a length equal to the perimeter of the base and a width equal to the height of the prism. Let's denote the height of the prism as "h". Therefore, the area of one of the lateral faces is given as 15h = 105 cm².

Dividing both sides by 15, we find that the height of the prism, h, is equal to 7 cm.

Now, we can calculate the volume of the prism. The volume of a prism is given by the formula V = base area × height. Since the base is a regular quadrilateral with side length 15 cm, the base area is 15² = 225 cm². Multiplying this by the height of 7 cm, we get:

V = 225 cm² × 7 cm = 1575 cm³.

Therefore, the volume of the regular quadrilateral prism is 1575 cm³.

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Answer: Let x be the cost of one slice of pizza and y be the cost of one soda.

From the problem, we know that:

6x + 4y = 37 ...(1)

4x + 6y = 33 ...(2)

To solve for x and y, we can use the method of elimination. Multiplying equation (1) by 3 and equation (2) by 2, we get:

18x + 12y = 111 ...(3)

8x + 12y = 66 ...(4)

Subtracting equation (4) from equation (3), we get:

10x = 45

Dividing both sides by 10, we get:

x = 4.50

Substituting this value of x into equation (1), we get:

6(4.50) + 4y = 37

Simplifying, we get:

27 + 4y = 37

Subtracting 27 from both sides, we get:

4y = 10

Dividing both sides by 4, we get:

y = 2.50

Therefore, one slice of pizza costs $4.50 and one soda costs $2.50.

Its components by their greatest common factor, which is 2:

To find a normal vector to the plane with the equation 8x - 14y - 6z = 0, we can simply read off the coefficients of x, y, and z and use them as the components of the normal vector. So, the normal vector is:

⟨8, -14, -6⟩

Note that this vector can be simplified by dividing all its components by their greatest common factor, which is 2:

⟨4, -7, -3⟩

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The service level is 6.6%, indicating the percentage of demand that can be met from current stock.

To calculate the service level, we need to use the service level formula, which is:

Service Level = (Demand During Lead Time + Safety Stock) / Average Demand

In this case, we are given the historical average demand, which is 6105 units with a standard deviation of 243. We are also given that the company currently has 6647 units in stock. We need to calculate the demand during the lead time and the safety stock.

Assuming the lead time is zero (i.e., we receive inventory instantly), the demand during the lead time is also zero. Therefore, the demand during lead time + safety stock = safety stock.

To calculate the safety stock, we can use the following formula:

Safety Stock = Z * Standard Deviation * Square Root of Lead Time

Where Z is the number of standard deviations from the mean that corresponds to the desired service level. For example, for a service level of 95%, Z is 1.645 (assuming a normal distribution).

Assuming a lead time of one day and a desired service level of 95%, we can calculate the safety stock as follows:

Safety Stock = 1.645 * 243 * sqrt(1) = 402.76

Substituting the values into the service level formula, we get:

Service Level = (0 + 402.76) / 6105 = 0.066 or 6.6%

Therefore, the service level is 6.6%.

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P = 3.2qThis is the equation that relates p and q when p varies directly with q.

When two variables are directly proportional to each other, they are said to be varying directly. This suggests that when one variable is multiplied by a fixed value, the other variable will also be multiplied by the same fixed value to obtain the product.

Let's say p is directly proportional to q. Then, we can write:  p = kq, where k is a constant of variation. We can obtain the equation that relates p and q by substituting the given values p = 9.6 and q = 3.  p = kq ⇒ 9.6 = k(3)

Solving for k:k = 9.6/3k = 3.2Now that we know k, we can substitute it back into the equation p = kq:p = 3.2q

This is the equation that relates p and q when p varies directly with q.

To confirm, let's check that it works for other values of p and q. If q = 2,p = 3.2(2) = 6.4If q = 5,p = 3.2(5) = 16

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In this case, homework is measured in points out of 100 and finals are measured in points out of 100, so the units for both the slope and y-intercept are "points per point."

Using the formula for the slope of the regression line:

b = r(SD of Y / SD of X)

where r is the correlation coefficient between X and Y, SD is the standard deviation, X is the predictor variable (homework), and Y is the response variable (finals).

Plugging in the values given in the table:

b = 0.5(15/8) = 0.9375

To find the y-intercept, we use the formula:

a = mean of Y - b(mean of X)

a = 65 - 0.9375(78) = -15.375

Therefore, the regression equation for predicting finals from homework is:

Finals = 0.94(Homework) - 15.38

Note that the units for the slope and y-intercept are determined by the units of the variables. In this case, homework is measured in points out of 100 and finals are measured in points out of 100, so the units for both the slope and y-intercept are "points per point."

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To apply the law of large numbers (LLN) to the average of Z, we need to make the following assumptions:

The observations Z1, Z2, ..., Zn are independent and identically distributed (iid).

The expected value E(Zi) exists and is finite for all i.

The LLN states that as the sample size n increases, the sample mean of the observations Z1, Z2, ..., Zn converges in probability to the expected value E(Zi):

lim (n → ∞) P(|(Z1 + Z2 + ... + Zn)/n - E(Zi)| > ε) = 0,

for any ε > 0.

In other words, as the sample size increases, the sample mean becomes a better and better estimate of the true expected value. The LLN provides a theoretical foundation for statistical inference, as it assures us that the sample mean is a consistent estimator of the population mean.

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The given Hexagon 1 reflected five different times and resulted in the dashed hexagons labeled as 2, 3, 4, 5, and 6.

The process of a reflection involves flipping a figure over a line to generate a mirror image of it.

A line of reflection is the line that the original figure is reflected across.

A dashed hexagon has a few unique characteristics that set it apart from a regular hexagon.

For Hexagon 1:When the given hexagon is reflected over the dotted line, it results in Hexagon 2.

Similarly, when the Hexagon 2 is reflected over the dotted line, it results in Hexagon

3. When we reflect Hexagon 3 over the dotted line, it results in Hexagon

4. Hexagon 4 can be mirrored to create Hexagon

5, and Hexagon 5 can be mirrored to create Hexagon

6. The dotted line can be described as a line of symmetry or reflectional symmetry.

.The dashed hexagons 2, 3, 4, 5, and 6 are all congruent to each other, with identical side lengths and angles.

In addition, the dashed hexagons are equilateral and equiangular.

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The travel time T between home and office is expected to be between 20 and 40 minutes depending upon traffic. Based on experience, the average travel time is 30 minutes and the corresponding variance is 20 minutes.What is the expected value of the travel time?The expected value of the travel time is the average of the travel time between the home and office, which is given as 30 minutes.What is the standard deviation of the travel time?The standard deviation of the travel time is the square root of the variance which is given as follows:Variance = 20 minutesStandard deviation = √Variance= √20= 4.47 minutes.What is the probability of travel time being less than 25 minutes?Let X be the random variable for travel time between home and office.X ~ N(30, 20)We need to find P(X < 25).First, we find the z-score as follows:z = (x - μ) / σz = (25 - 30) / 4.47z = -1.12Using a standard normal distribution table, we can find the probability as:P(X < 25) = P(Z < -1.12) = 0.1314Therefore, the probability of travel time being less than 25 minutes is 0.1314.

a) The expected travel time is : 30 minutes.

b) The standard deviation of travel times is: 4.47 minutes

c) The probability that the travel time is less than 25 minutes is 0.1314.  

a) The expected travel time is simply the average travel time between home and office, given as 30 minutes.

b) The standard deviation of travel times is simply the square root of the variance and is expressed as:

Difference = 20 minutes

therefore:

standard deviation = √variance

standard deviation = √20

Standard deviation = 4.47 minutes.

c) Let X be the random variable for travel time between home and office. X to N(30,20)

I need to find P(X < 25).

First, find the Z-score from the following formula:

z = (x - μ)/σ

z = (25 - 30)/4.47

z = -1.12

The probabilities from the online p-values ​​in the Z-score calculator are:

P(X < 25) = P(Z < -1.12) = 0.1314

Therefore, the probability that the travel time is less than 25 minutes is 0.1314.  

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Complete question is:

The travel time T between home and office is expected to be between 20 and 40 minutes depending upon traffic. Based on experience, the average travel time is 30 minutes and the corresponding variance is 20 minutes.

What is the expected value of the travel time?

What is the standard deviation of the travel time?

What is the probability of travel time being less than 25 minutes?