A sociologist is studying the number of years of education of students whose mothers have bachelor's degrees or higher. The data is normally distributed with a population mean of 14.5 years and a population standard deviation of 2.5 years. If a sample of 55 students is selected at random from the population, select the mean and standard deviation of the sampling distribution below.

a. σi= 0.05 years
b. σi= 2.5 years
c. σi= 0.34 years
d. µ= 14.5 years

Answer:

[tex]y = -\frac{7x}{3} - 24[/tex]

Step-by-step explanation:

We can model this function using the equation of a line:

[tex]y = ax + b[/tex]

Where a is the slope of the line and b is the y-intercept.

To find the values of a and b, we can use the two points given:

(-9, -3):

[tex]-3 = a * (-9) + b[/tex]

[tex]-9a + b = -3[/tex]

(-12, 4):

[tex]4 = a * (-12) + b[/tex]

[tex]-12a + b = 4[/tex]

If we subtract the second equation from the first one, we have:

[tex]-12a + b - (-9a + b) = 4 - (-3)[/tex]

[tex]-12a + 9a = 4 + 3[/tex]

[tex]-3a = 7[/tex]

[tex]a = -7/3[/tex]

Then, finding the value of b, we have:

[tex]-12a + b = 4[/tex]

[tex]28 + b = 4[/tex]

[tex]b = -24[/tex]

So the equation is:

[tex]y = -\frac{7x}{3} - 24[/tex]

Answer: Undefined

Step-by-step explanation:

For this problem, we know that 3ˣ=-9. All we have to do is figure out what x is.

We know that any integer raised to the power cannot be negative. The closest answer we can get is x=2 because 3²=9. Unfortunately, we are looking for -9. Therefore, this x is undefined.

Answer: The number of quarter inches in 23 inches is 4 × 23 = 92

None of the answers given is correct.

Step-by-step explanation:

The ÷ sign means divide.

There are 4 quarter inches in each inch, so you have to multiply 23 × 4

Dividing by 14 makes no sense.

23 ÷ 1/4 = 92 is also an equation that makes sense.

Answer:

[tex](x-3)^2=4[/tex]

Step-by-step explanation:

Tara's work is shown below:

[tex]\begin{aligned} 2(x-3)^2+6&=14 \\\\ 2(x-3)^2&=8&\text{Step }1 \\\\ &&\text{Step }2 \\\\ x-3&=\pm 2&\text{Step }3 \\\\ x=1&\text{ or }x=5&\text{Step }4 \end{aligned}[/tex]

From the equation, we notice that in Step 1, Tara did:

[tex]2(x-3)^2+6=14\\2(x-3)^2=14-6\\2(x-3)^2=8[/tex]

She is trying to isolate the x-variable. Therefore, the next logical step will be to divide both sides by 2 and her Step 2 will therefore be:

[tex]\dfrac{2(x-3)^2}{2} =\dfrac{8}{2} \\\\(x-3)^2=4[/tex]

Tara could have written: [tex](x-3)^2=4[/tex] as her step 2 and we would then have her work as:

[tex]\begin{aligned} 2(x-3)^2+6&=14 \\\\ 2(x-3)^2&=8&\text{Step }1 \\\\ (x-3)^2&=4&\text{Step }2 \\\\ x-3&=\pm 2&\text{Step }3 \\\\ x=1&\text{ or }x=5&\text{Step }4 \end{aligned}[/tex]

Answer:

Step 2

Step-by-step explanation:

I did the Khan Academy.

Answer:

The sample correlation coefficient is, r = 0.8722.

The equation of the least-squares line is:

[tex]y= -0.161+0.154x[/tex]

Step-by-step explanation:

(a)

The scatter diagram displaying the data for X : total number of jobs in a given neighborhood and Y : number of entry-level jobs in the same neighborhood is shown below.

(b)

The table attached below verifies the values of [tex]\sum X,\ \sum Y,\ \sum X^{2},\ \sum Y^{2}\ \text{and}\ \sum XY[/tex].

The sample correlation coefficient is:

[tex]\begin{aligned}r~&=~\frac{n\cdot\sum{XY} - \sum{X}\cdot\sum{Y}} {\sqrt{\left[n \sum{X^2}-\left(\sum{X}\right)^2\right] \cdot \left[n \sum{Y^2}-\left(\sum{Y}\right)^2\right]}} \\r~&=~\frac{ 6 \cdot 1163 - 201 \cdot 30 } {\sqrt{\left[ 6 \cdot 7759 - 201^2 \right] \cdot \left[ 6 \cdot 182 - 30^2 \right] }} \approx 0.8722\end{aligned}[/tex]

Thus, the sample correlation coefficient is, r = 0.8722.

(c)

The slope and intercept are:

[tex]\begin{aligned} a &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 30 \cdot 7759 - 201 \cdot 1163}{ 6 \cdot 7759 - 201^2} \approx -0.161 \\ \\b &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 6 \cdot 1163 - 201 \cdot 30 }{ 6 \cdot 7759 - \left( 201 \right)^2} \approx 0.154\end{aligned}[/tex]

The equation of the least-squares line is:

[tex]y= -0.161+0.154x[/tex]

(d)

The least-squares line is graphed in the diagram below.

Answer:

He served as Assistant Secretary of the Navy under President William McKinley

hope i helped

-lvr

Answer:

[tex] \boxed{\sf Final \ velocity \ (v) = 26 \ m/s} [/tex]

Given:

[tex] \sf v = v_{0} + at[/tex]

[tex]\sf Initial \ velocity \ (v_{0}) = 20 \ m/s \\ \sf Acceleration \ (a) = 1.5 \ m/s^{2} \\ \sf Time \ (t) = 4 \ sec[/tex]

To Find:

Final velocity (v)

Step-by-step explanation:

[tex]\sf Substituting \ value \ of \ Initial \ velocity \\ \sf acceleration \ and \ time \ in \ given \ equation: \\ \\ \sf \implies v = v_{0} + at \\ \\ \sf \implies v = 20 + 1.5(4) \\ \\ \sf 1.5 \times 4 = 6 : \\ \sf \implies v = 20 + \boxed{6} \\ \\ \sf 20 + 6 = 26 : \\ \sf \implies v = 26 \: m/s[/tex]

Answer:

9

Step-by-step explanation:

f(x) = (x + 1)^2

Let x=2

f(2) = (2 + 1)^2

     = 3^2

     = 9

Answer:

The probability would be 40 / 500 = 0.08.

Answer:

25/88

Step-by-step explanation:

25 red marbles, 27 blue marbles, and 36 yellow marbles. = 88 marbles

P(red) = number of red/total

          = 25/88

Answer:

Dear user,

Answer to your query is provided below

Probability of choosing a red marble is 0.28 or (25/88)

Step-by-step explanation:

Total number of marbles = 88

Number of red marbles = 25

Probability = 25/88

Answer:

(a) The probability that at least one individual with a reservation cannot be accommodated on the trip is 0.4202.

(b) The expected number of available places when the limousine departs is 0.338.

Step-by-step explanation:

Let the random variable Y represent the number of passenger reserving the trip shows up.

The probability of the random variable Y is, p = 0.70.

The success in this case an be defined as the number of passengers who show up for the trip.

The random variable Y follows a Binomial distribution with probability of success as 0.70.

(a)

It is provided that n = 6 reservations are made.

Compute the probability that at least one individual with a reservation cannot be accommodated on the trip as follows:

P (At least one individual cannot be accommodated) = P (X = 5) + P (X = 6)

[tex]={6 \choose 5}\ (0.70)^{5}\ (1-0.70)^{6-5}+{6 \choose 6}\ (0.70)^{6}\ (1-0.70)^{6-6}\\\\=0.302526+0.117649\\\\=0.420175\\\\\approx 0.4202[/tex]

Thus, the probability that at least one individual with a reservation cannot be accommodated on the trip is 0.4202.

(b)

The formula to compute the expected value is:

[tex]E(Y) = \sum X\cdot P(X)[/tex]

[tex]P (X=0)={6 \choose 0}\ (0.70)^{0}\ (1-0.70)^{6-0}=0.000729\\\\P (X=1)={6 \choose 1}\ (0.70)^{1}\ (1-0.70)^{6-1}=0.010206\\\\P (X=2)={6 \choose 2}\ (0.70)^{2}\ (1-0.70)^{6-2}=0.059535\\\\P (X=3)={6 \choose 3}\ (0.70)^{3}\ (1-0.70)^{6-3}=0.18522\\\\P (X=4)={6 \choose 4}\ (0.70)^{4}\ (1-0.70)^{6-4}=0.324135[/tex]

Compute the expected number of available places when the limousine departs as follows:

[tex]E(Y) = \sum X\cdot P(X)[/tex]

         [tex]=(4\cdot 0.000729)+(3\cdot 0.010206)+(2\cdot 0.059535)+(1\cdot 0.18522)\\+(0\cdot 0.324135)\\\\=0.002916+0.030618+0.11907+0.18522+0\\\\=0.337824\\\\\approx 0.338[/tex]

Thus, the expected number of available places when the limousine departs is 0.338.

Answer:

please see the attached picture for full solution

Hope it helps

Good luck on your assignment

Answer:

C. G(x)= x³ + 1

Step-by-step explanation:

The graph has moved to right by one point so the function is:

G(x)= x³ + 1

option C is correct

Answer:

The future value of the annuity due to the nearest cent is $2956.

Step-by-step explanation:

Consider the provided information:

It is provided that monthly payment is $175, interest is 7% and time is 11 years.

The formula for the future value of the annuity due is:

Now, substitute P = 175, r = 0.07 and t = 11 in above formula.

Hence, the future value of the annuity due to the nearest cent is $2956.

Step-by-step explanation:

Answer:

Function

Step-by-step explanation:

y = 1/3 x - 4

Is a function because for every x, we will get only one value of y.

Answer:

Yes,is a function

We can obtain the points (0,-4)(6,-2)

I hope this help you :)......  

Answer: Her scores in one game may be 5 points and the other may be 4 points.

Step-by-step explanation:

You may think about dividing the 9 points into two to find how many points she made in each game. But after dividing you will have 4.5 which is not an accurate answer.In a basketball game you can't score have a point but you make whole points.

Answer:

(a) S = {GH, GT, BH, BT, RH and RT}

(b) The value of P (A) is 0.15.

(c) A and B mutually exclusive.

(d) A and C are not mutually exclusive.

Step-by-step explanation:

There are 10 cards in a special deck of cards: 4 are green (G), 3 are blue (B), and 3 are red (R).

Also when a card is picked, its color of it is recorded. An experiment consists of first picking a card and then tossing a coin.

(a)

The sample space is:

S = {GH, GT, BH, BT, RH and RT}

(b)

A = a blue card is picked first, followed by landing a head on the coin toss

Compute the probability of event A as follows:

[tex]P(A)=P(B)\times P(H)[/tex]

         [tex]=\frac{3}{10}\times\frac{1}{2}\\\\=\frac{3}{20}\\\\=0.15[/tex]

Thus, the value of P (A) is 0.15.

(c)

B = a red or green is picked, followed by landing a head on the coin toss.

The result of the coin toss is same for both events A and B.

So, consider the events,

A as a blue card is picked first

B as a red or green is picked

There is no intersection point for the two events.

Thus, events A and B mutually exclusive.

(d)

C = a red or blue is picked, followed by landing a head on the coin toss.

The result of the coin toss is same for both events A and C.

So, consider the events,

A as a blue card is picked first

C as a red or blue is picked

There is an intersection point for the two events.

Thus, events A and C are not mutually exclusive.

Part(a): The sample space can be written as shown below:

[tex]S=\{GH,GT,BH,BT,RH,RT\}[/tex]

Part(b): The required probability is [tex]P(A)=0.15[/tex]

Part(c): The events A and B are mutually exclusive because of [tex]P( A\ AND\ B ) = 0[/tex] are equal to zero.

Part(d): The events A and C are not mutually exclusive because [tex]P( A\ AND\ C ) = 0[/tex] are not equal to zero.

A sample space is a collection of a set of possible outcomes of a random experiment. The sample space is represented using the symbol, “S”.

Part(a):

A special deck contains ten cards with colors red, green, and blue when the card is picked its color gets recorded, and after that coin will get tossed.

Then the sample space can be written as shown below:

[tex]S=\{GH,GT,BH,BT,RH,RT\}[/tex]

Part(b):

If A is the event that a blue card is picked first followed by landing ahead on the coin toss then the outcome it contains is 3 blue cards and 1 head.

Therefore the [tex]P(A)[/tex] is calculated below:

[tex]P(A):P(B)\timesP(H)\\=\frac{3}{10}\times\frac{1}{2}\\ =0.15[/tex]

Part(c):

Mutually exclusive events contain a probability [tex]P( A\ AND\ B ) = 0[/tex] that means there is no common outcome between them.

Here, it can be noticed that events A and B cannot happen at the same time. That means, the researcher cannot pick the same cards together. Either it could be red or green.

Hence, events A and B are mutually exclusive because of [tex]P( A\ AND\ B ) = 0[/tex] are equal to zero.

Part(d):

Mutually exclusive events contain a probability [tex]P( A\ AND\ C ) = 0[/tex]  which means there is no common outcome between them.

Here, it can be noticed that events A and C can happen at the same time because event C can contain all outcomes of event A.

Hence, events A and C are not mutually exclusive because [tex]P( A\ AND\ C ) = 0[/tex] are not equal to zero.

Learn more about the topic samples space:

https://brainly.com/question/10684603

Answer:

Step-by-step explanation:

Hi,

the function is defined for all reals so the domain is [tex]]-\infty;+\infty[[/tex]

for x real

|x| >= 0

so f(x) >= 4

so the range is [tex][4;+\infty[[/tex]

do not hesitate if you need any further explanation

hope this helps

Answer:

Domain: (-∞,∞) Range: (4,∞)

Answer:

the correct answer is

Step-by-step explanation:

So, the probability is:P(greater than 4)=26=13. This is a theoretical probability, which is the observed number of favorable outcomes out of a certain number of trials. For instance, suppose you rolled the six-sided die five times, and got the following results:2,6,4,5,6

hope this help you!!!!!

Answer:

1/5 chance.

Step-by-step explanation:

There is only one number, 5, that is greater than 4 and there are 5 total numbers so there is a 1/5 chance selecting that number.

Answer: The distance of the shortest route of return is 400

Step-by-step explanation:

The direction of travel of the plane forms a right angle triangle ABC as shown in the attached photo. C represents the starting point of the plane. To determine the distance of the shortest by which the plane can return to its starting point, BC, we would apply the Pythagorean theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

BC² = 320² + 240²

BC² = 160000

BC = √160000

BC = 400

Answer:

a.) 8x + 6y

b.) 4x + 2y

Step-by-step explanation:

Simply add like terms together (x with x and y with y).

Answer:

A and B

Step-by-step explanation:

The surface area is found by calculating the 6 faces of a 3-d object. Since A and B are the only ones that cause you to use the whole object for the given task the answers are A and B.

Answer: The other person is correct its A and B

Explanation:

Answer:

44.43% probability that among 40 adults (ages 70 and older) chosen at random more than 22 percent will have been told by their doctor that they have cancer

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this question, we have that:

[tex]p = 0.211, n = 40[/tex]

So

[tex]\mu = 0.211, s = \sqrt{\frac{0.211*0.789}{40}} = 0.0645[/tex]

What is the probability that among 40 adults (ages 70 and older) chosen at random more than 22 percent will have been told by their doctor that they have cancer

This is 1 subtracted by the pvalue of Z when X = 22. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.22 - 0.211}{0.0645}[/tex]

[tex]Z = 0.14[/tex]

[tex]Z = 0.14[/tex] has a pvalue of 0.5557

1 - 0.5557 = 0.4443

44.43% probability that among 40 adults (ages 70 and older) chosen at random more than 22 percent will have been told by their doctor that they have cancer

Answer:

C.

Step-by-step explanation:

The seats are counted by 1 for both tricycles and bicycles, so t + b has to equal 35. The only answer choice that has t + b = 35 is C.

Answer:

0.6 = 60% probability that the waiting time for this train is more than 4 minutes on a given day

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X higher than x is given by the following formula.

[tex]P(X > x) = \frac{b - x}{b-a}[/tex]

The waiting time for a train has a uniform distribution between 0 and 10 minutes.

This means that [tex]a = 0, b = 10[/tex]

What is the probability that the waiting time for this train is more than 4 minutes on a given day?

[tex]P(X > x) = \frac{b - x}{b-a}[/tex]

[tex]P(X > 4) = \frac{10 - 4}{10 - 0} = 0.6[/tex]

0.6 = 60% probability that the waiting time for this train is more than 4 minutes on a given day

Answer:

39

Step-by-step explanation:

12+20+22+22+23=99

new mean=23

23*6=138

138-99=39

a) - The numbers are in row order.

Male -  12, 23, 3, 38

Female - 35, 9, 18, 62

Total - 47, 32, 21, 100

b) - 23 Males drank only coffee.

c) - 62 Women participated in the survey.

d) - 47 people drank only tea.

It's just math, gotta do some adding.  

Answer:

Step-by-step explanation:

b) 9 + x = 32

Therefore 32 - 9 = 23

c) The total number of females: 100-38 = 62

d)  The number of females who drink tea is 62 - (18 +9) = 35

Answer:

The calculated  value Z = 3.775 > 1.96 at 0.05 level of significance

Null hypothesis is rejected

The Two Population proportion are not equal

Step-by-step explanation:

Given first sample size n₁ = 677

First sample proportion

                             [tex]p^{-} _{1} = \frac{x_{1} }{n_{1} } = \frac{172}{677} = 0.254[/tex]

Given second sample size n₂ = 3377

second sample proportion

                             [tex]p^{-} _{2} = \frac{x_{2} }{n_{2} } = \frac{654}{3377} = 0.1936[/tex]

Null Hypothesis : H₀ :  p₁ = p₂.

Alternative Hypothesis : H₁ :  p₁ ≠ p₂.

      Test statistic

                [tex]Z = \frac{p_{1} ^{-}-p^{-} _{2} }{\sqrt{P Q(\frac{1}{n_{1} } +\frac{1}{n_{2} }) } }[/tex]

where

        [tex]P = \frac{n_{1} p_{1} + n_{2} p_{2} }{n_{1}+n_{2} } = \frac{677 X 0.254+3377 X 0.1936}{677+3377}[/tex]

       P =  0.2036

      Q = 1 - P = 1 - 0.2036 = 0.7964

         [tex]Z = \frac{0.254- 0.1936 }{\sqrt{0.2036 X 0.7964(\frac{1}{677 } +\frac{1}{3377 }) } }[/tex]

        Z =  3.775

Critical value ∝=0.05

Z- value = 1.96

The calculated  value Z = 3.775 > 1.96 at 0.05 level of significance

Null hypothesis is rejected

The Two Population proportion are not equal

Answer:

72√3

Step-by-step explanation:

30 60 90 triangles are what you start out with.

Step 1: 30-60-90

x = 12

WZ = 12√3

Step 2: Area formula

A = 1/2(12)(12√3)

*Since the 2 30-60-90 triangles are congruent, both segments of the base are 12

Plug it into the calc and you should get A = 72√3 as your final answer!