Answer:
a) This is the p-value of Z when X = A subtracted by the p-value of Z when X = B.
b) P-value of Z when X = 76 subtracted by the p-value of X = 68.
c) Because the underlying distribution(pulse rates of females) is normal.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes 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.
In this question:
Mean [tex]\mu[/tex], standard deviation [tex]\sigma[/tex].
standard deviation of beats per minute.
a. If 1 adult female is randomly selected, find the probability that her pulse rate is between A beats per minute and B beats per minute.
This is the p-value of Z when X = A subtracted by the p-value of Z when X = B.
b. If 4 adult females are selected, find the probability that they have pulse rates with a mean between 68 beats per minute and 76 beats per minute.
Sample of 4 means that we have [tex]n = 4, s = \frac{\sigma}{\sqrt{4}} = 0.5\sigma[/tex]
The formula for the z-score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{X - \mu}{0.5\sigma}[/tex]
[tex]Z = 2\frac{X - \mu}{\sigma}[/tex]
This probability is the p-value of Z when X = 76 subtracted by the p-value of X = 68.
c. Why can the normal distribution be used in heartbeat even the sample side does not exceed 30?
Because the underlying distribution(pulse rates of females) is normal.
The product of nine, x and y
Answer:
(9)(x)(y) or 9(x + y)
Step-by-step explanation:
Question 20
Josh says that has the same quotient as Is this true or false?
O True
O False
5. The Toy Car Company sells toy cars for $8.00
per car and charges $3.50 for shipping.
Answer:
$11.50
Step-by-step explanation:
A town recently dismissed 88 employees in order to meet their new budget reductions. The town had 77 employees over 5050 years of age and 1717 under 5050. If the dismissed employees were selected at random, what is the probability that at least 66 employees were over 5050? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answer:
0.0013 probability that at least 6 employees were over 50.
Step-by-step explanation:
The employees were "chosen" to be dismissed without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x sucesses is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of sucesses.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem:
8 employees dismissed means that [tex]n = 8[/tex]
Had 7 + 17 = 24 employees, which means that [tex]N = 24[/tex]
7 over 50, which means that [tex]k = 7[/tex]
What is the probability that at least 6 employees were over 50?
6 or 7, so:
[tex]P(X \geq 6) = P(X = 6) + P(X = 7)[/tex].
In which
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 6) = h(6,24,8,7) = \frac{C_{7,6}*C_{17,2}}{C_{24,8}} = 0.0013[/tex]
[tex]P(X = 7) = h(7,24,8,7) = \frac{C_{7,7}*C_{17,1}}{C_{24,8}} \approx 0[/tex]
[tex]P(X \geq 6) = P(X = 6) + P(X = 7) = 0.0013 + 0 = 0.0013[/tex]
0.0013 probability that at least 6 employees were over 50.
HELP
Which equation has no real solution A. B2 + 3b = -3
B. 2c2 + 4c = 9
C. -5c2 – c= -2
D.7g +1 + 3g2 = 0
Answer:
A.
[tex] {b}^{2} + 3b - 3 = 0[/tex]
Step-by-step explanation:
[tex] {b}^{2} + 3b - 3 = 0 \\ because \: \: {b}^{2} < 4ac \\ {b}^{2} = {3}^{2} = 9 \\ 4ac = 4 \times 1 \times - 3 = - 12 \\ hence : {b}^{2} < 4ac[/tex]
]This problem is for my math class
Solve the inequality below
6x - 5 < 55
Answer: x < 10
Step-by-step explanation: Just like any of your two-step equations, in this inequality, start by isolating the x term which in this case is 6x by adding 5 to both sides.
That leaves you with 6x < 60 and now just divide both sides by 2 and x < 10.
Notice that because we divide both sides of the inequality
by a positive number, not a negative, we did not change the
direction of the inequality sign.
Finally, put your answer in set notation, {x: x < 10}.
Unlike an equation which normally has one solution, the answer to an inequality must be stated as a solution set because an entire set of answers will work. In this problem, it's any number less than 10.
PLEASE HELP ASAP Use the figure to complete the following trigonometric ratios.
Answer:
[tex]sinB=\frac{15}{17} , cos B=\frac{8}{17} , tanB=\frac{15}{8} \\sinA=\frac{8}{17} , cos A=\frac{15}{17} , tanA=\frac{8}{15}[/tex]
Step-by-step explanation:
[tex]sinB=\frac{15}{17} , cos B=\frac{8}{17} , tanB=\frac{15}{8} \\sinA=\frac{8}{17} , cos A=\frac{15}{17} , tanA=\frac{8}{15}[/tex]
solve for x:
x + 2 1/3 = 3 1/5
x-2 2/3 = 5/6
Convert 15meter to 5kilometer
Answer:
Step-by-step explanation:
1 m =0.001 km
15m=15*0.001
=0.015 km
Find the median and mean of the data set below:
25, 13, 6, 4,2
Answer: im sorry but there is nothing here to help? may you add a picture? or something file maybe?
Step-by-step explanation:
Calculate the volume of this prism.
67-2x+89/2+7-8x=0
help me please
Answer:
x = 11.85
Step-by-step explanation:
[tex]67 - 2x + \frac{89}{2} + 7 -8x = 0\\\\67 + \frac{89}{2}+7 = 8x + 2x\\\\\frac{134 + 89 +14}{2} = 10x\\\\10x = 118.5\\\\x = 11.85[/tex]
Answer:
[tex]x = 11 \frac{17}{20}[/tex] or [tex]\frac{237}{20}[/tex]
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Simplify the expression
2(6x + 3)
Need some help on this
9514 1404 393
Answer:
a. set 1: 29 minutes; set 2: 25 minutes
b. set 1 is more challenging than set 2
Step-by-step explanation:
a. The mean is found by adding the times and dividing by the number of times. For set 1, that is ...
(2×27 +2×28 +3×29 +2×30 +33)/10 = 290/10 = 29 . . . minutes
For set 2, that is ...
(4x24 +4×25 +2×27)/10 = 250/10 = 25 . . . minutes
__
b. The mean of set 1 is higher, and the spread is wider, suggesting more students have more trouble with the problems of set 1. That is, ...
set 1 is more challenging than set 2
Keano and Emily are going to Europe to buy some shoes, they will need €1500. How many American Dollars will it take to get that much, knowing that the exchange rate of USD: EUR is €1: $1.14 *
Answer:
1710
Step-by-step explanation:
you will multiply 1500 euros by the exchange rate
A cable 27 feet long runs from the top of a utility pole to a point on the ground 16 feet from the base of the pole. How tall is the utility pole?
Answer:
15^2+x^2=22^2
225+x^2=484
x^2=259
x=16.09 feet
Step-by-step explanation: 15^2+x^2=22^2
225+x^2=484
x^2=259
x=16.09 feet
45-45-90 Right Triangles! Can somebody please help me? ASAP!!
Answer:
Step-by-step explanation:
45-45-90 triangles always have the same relationships
leg = x, hypotenuse = x√2
If you have the leg length multiply it by √2 to get the hypotenuse
hypotenuse = x, Leg = x/√2
If you have the hypotenuse length divide it by √2 to get the leg
-----------------------
7)
leg = 3√2 / 2
hyp = 3√2 / 2 * √2 = 3
8)
leg = 5√2
hyp = 5√2 *√2 = 10
9)
hyp = 2
leg = 2 / √2 = √2
10)
leg = 13√2 / 2
hyp = 13√2 / 2 * √2 = 13
11)
leg = 3√3
hyp = 3√3 * √2 = 3√6
12)
leg = 12
hyp = 12√2
Determine the slope of the line passing through (4, -2) and (7, 10).
Answer:
4
Step-by-step explanation:
To find slope without a graph, you subtract the 2 y-coords and the 2 x-coords, then divide the y-coord by the x-coord.
The formula is (y²-y¹)/(x²-x¹).
So we just plug in the coordinates.
(10-(-2))/(7-4)
(10+2)/(7-4)
12/3
4
So the slope is 4.
---
hope it helps
The slope of the line passing through (4, -2) and (7, 10) is,
⇒ m = 4
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
We have to given that;
Two points on the line are (4, -2) and (7, 10).
Since, The equation of line passes through the points (4, -2) and (7, 10).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (10 - (-2)) / (7 - 4)
m = 12 / 3
m = 4
Thus, The slope of line = 4
Learn more about the equation of line visit:
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I need help on this question
Answer:
A
Step-by-step explanation:
A cupcake recipe takes 3 cups of flour for every 2 dozen cupcakes. How many cups of flour does Sally need to make 96 cupcakes? Use the table to help.
Answer: 12 cups of flour
Step-by-step explanation:
12 cups of flour 3 + 3 + 3 + 3 = 12 because I have to make 96 cupcakes for tomorrow.
The amount of flour required will be 8 x 1.5 = 12 cups of flour. Option A is correct.
What is the Ratio?The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.
To make 2 dozen cupcakes, the recipe requires 3 cups of flour. Therefore, for 1 dozen cupcakes, the recipe requires 1.5 cups of flour (since 2 dozen cupcakes = 2 x 1.5 = 3 cups of flour).
To make 96 cupcakes, Sally needs 8 dozen cupcakes (since 8 x 12 = 96). Therefore, the amount of flour required will be 8 x 1.5 = 12 cups of flour.
So, the answer is 12 cups of flour, and the explanation should be:
To make 2 dozen cupcakes, the recipe requires 3 cups of flour. Therefore, for 1 dozen cupcakes, the recipe requires 1.5 cups of flour. To make 96 cupcakes, Sally needs 8 dozen cupcakes.
Therefore, the amount of flour required will be 8 x 1.5 = 12 cups of flour.
Learn more about Ratio here:
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The mean of a standard normal probability distribution _____. a. can be any value b. can be any value as long as it is positive c. is always equal to 1 d. None of these answers are correct.
Answer:
D
Step-by-step explanation:
The mean of a standard normal distribution is always = 0 with the standard deviation being equal to. Therefore a standard normal distribution is a normal distribution described with a mean of 0 and standard deviation of 1. Since a standard normal distribution is centered at the middle with equal distribution to both the left and right of the distribution. The centre point is 0, which is the mean and the standard deviation is 1 to either side of the distribution.
Given P(A) = 0.3, P(B) 0.63 and P(BA) = 0.79, find the value of
P(A and B), rounding to the nearest thousandth, if necessary.
Answer:
P(A and B) = 0.14.
Step-by-step explanation:
Venn probabilities:
Suppose we have two events, A and B. The probability P(A and B) is given by:
[tex]P(A \cap B) = P(A) + P(B) - P(A \cup B)[/tex]
In which [tex]P(A \cup B)[/tex] is P(A or B).
In this question:
P(A) = 0.3, P(B) = 0.63, P(A or B) = 0.79. So
[tex]P(A \cap B) = P(A) + P(B) - P(A \cup B) = 0.3 + 0.63 - 0.79 = 0.93 - 0.79 = 0.14[/tex]
So
P(A and B) = 0.14.
If f(x)=5^x+2x and g(x)=3x-6
find (f+g)(x)
Answer:
(f+g)(x) = 5^x+5x-6
Step-by-step explanation:
f(x)=5^x+2x
g(x)=3x-6
(f+g)(x) = 5^x+2x+3x-6
Combine like terms
(f+g)(x) = 5^x+5x-6
Determine the missing angle in the picture below.
Answer:
x =41.18114952
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
We know the hypotenuse and adjacent sides
cos theta = adjacent / hypotenuse
cos x = 14.3/19
taking the inverse cos of each side
cos^-1 (cos x) = cos ^-1 ( 14.3/19)
x =41.18114952
Answer:
Step-by-step explanation:
take x degree as reference angle
using cos rule
cos x=adjacent/hypotenuse
cos x=14.3/19
cos x=0.75
x=cos 41
x= 41 degree
Estimate the given product 61 x 47 =
A = 7x2 - 3x + 10
B = -4x2 + 6x - 4
A - B =
Your answer should be a polynomial in standard form.
Answer:
A - B = 11x² -9x + 14
A - B = 11x² -9x + 14
Which graph represents the equation (x – 3)2 + y2 = 16?
Answer:
It is B on edge
Step-by-step explanation:
Mary’s bedroom rug is shown below. Find the perimeter and area of the rug.
pls help alot of points
Answer:
the perimeter is given in__in__, the height in_in___, and area of the base in_in²__.
so
none of the above.
Answer:
d
Step-by-step explanation:
none of the above
You have inherited land that was purchased for $25,000 in 1970. The value of the land has appreciated by
approximately 4% per year. What was the value of the land in the year 2000?
(a) Write the exponential function for this scenario:
(b) What was the value of the land in the year 2000? Round to the nearest whole dollar.
A. $750,000
B. $605,035,808
C. $81,084
D. $7,346
Answer:
Future value of land = 25,000[1.04]³⁰
Future value of land = $81,084 (Approx.)
Step-by-step explanation:
Given:
Purchase cost of land in 1970 = $25,000
Application rate = 4% per year
Find:
Price of land in 2000
Computation:
Number of year = 2000 - 1970 = 30 year
Future value of land = [Purchase cost of land][1+Application rate]ⁿ
F = P[1+r]ⁿ
Future value of land = 25,000[1+4%]³⁰
Future value of land = 25,000[1+0.04]³⁰
Future value of land = 25,000[1.04]³⁰
Future value of land = 25,000[3.24339]
Future value of land = 81,084.75
Future value of land = $81,084 (Approx.)