# Assignment 4A 1) The average age of CEO’s is 56 years. Assume the variable is normally distributed. If the standard deviation is 4 years, find the probability that the age of a randomly selected CEO...

Assignment 4A
1) The average age of CEO’s is 56 years. Assume the variable is normally distributed. If the standard deviation is 4 years, find the probability that the age of a randomly selected CEO will satisfy each condition:
a) be less than 50 years old
b) be more than 57.5 years old
c) be between 49 and 67 years old.
2) The average charitable contribution deduction on federal tax returns for the year 2007 was \$625. Suppose that the distribution of contributions is normal with a standard deviation of \$100. Find the limits for the middle 60% of contributions.
3) In a normal distribution, find when is 6 and 3.75% of the area lies to the left of 85.
4) The average teacher’s salary in timbucktoo is \$29,863. Assume a normal distribution with a standard deviation of \$5000.
a) What is the probability that a randomly selected teacher’s salary is greater than \$32,500?
b) For a sample of 70 teachers’, what is the probability that the sample mean will be greater than \$32,500?
c) Explain why your answers to parts a) and b) are different.
Assignment 4B
1) Use the normal approximation to the binomial to find the probability of X = 20 when n = 30 and p = 0.5.
2) Of all 3 – 5 year old children, 71% are enrolled in school. If a sample of 400 children are randomly selected, what is the probability that at least 300 will be enrolled in school.
3) 5% of theater patrons do not show up for the performance. If the theater has 120 seats, what is the probability that 6 or more will not show up to a particular performance.
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Assignment 4A XXXXXXXXXXThe average age of CEO’s is 56 years. Assume the variable is normally distributed. If the standard deviation is 4 years, find the probability that the age of a randomly selected CEO will satisfy each condition:a) be less than 50 years oldb) be more than 57.5 years oldc XXXXXXXXXXbe between 49 and 67 years old. XXXXXXXXXXThe average charitable contribution deduction on federal tax returns for the year 2007 was \$625. Suppose that the distribution of contributions is normal with a standard deviation of \$100. Find the limits for the middle 60% of contributions. XXXXXXXXXXIn a normal distribution, find when is 6 and 3.75% of the area lies to the left of 85. XXXXXXXXXXThe average teacher’s salary in timbucktoo is \$29,863. Assume a normal distribution with a standard deviation of \$5000. a) What is the probability that a randomly selected teacher’s salary is greater than \$32,500?b) For a sample of 70 teachers’, what is the probability that the sample mean will be greater than \$32,500?c XXXXXXXXXXExplain why your answers to parts a) and b) are different. Assignment 4B XXXXXXXXXXUse the normal approximation to the binomial to find the probability of X = 20 when n = 30 and p = 0.5. XXXXXXXXXXOf all 3 – 5 year old children, 71% are enrolled in school. If a sample of 400 children are randomly selected, what is the probability that at least 300 will be enrolled in school. XXXXXXXXXX% of theater patrons do not show up for the performance. If the theater has 120 seats, what is the probability that 6 or more will not show up to a particular performance.

## Solution

Robert answered on Dec 20 2021
NOTE FOR CALCULATING PROBABILITIES WE CAN USE ONLINE CALCULATORS USING
http:
stattrek.com/online-calculato
normal.aspx
http:
easycalculation.com/statistics
inomial-distribution.php
1) The average age of CEO’s is 56 years. Assume the variable is normally distributed. If the standard deviation is 4 years, find the probability that the age of a randomly selected CEO will satisfy each condition:
Let X denote age of a CEO
a) be less than 50 years old
P(X<50) = P(z < (50-56)/4)) = P(z< -1.5) = 0.0668
) be more than 57.5 years old
P(X>57.5) = P(z > (57.5-56)/4)) = P(z>.375) = .352
c) be between 49 and 67 years old.
P(492) The average charitable contribution deduction on federal tax returns for the year 2007 was \$625. Suppose that the distribution of contributions is normal with a standard deviation of \$100. Find the limits for the middle 60% of contributions.
Let the middle values for 60% lie between...
SOLUTION.PDF