BUSI 230 HW 7.3 Sampling Distributions and the Central Limit Theorem Assignment solutions answers

BUSI 230 HW 7.3 Sampling Distributions and the Central Limit Theorem Assignment solutions complete answers 

 

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Select the appropriate word or phrase to complete the sentence.

The probability distribution of  is called a  distribution.

states that the sampling distribution of  is approximately normal when the sample is large.

 

A sample of size 125 will be drawn from a population with mean 50 and standard deviation 17. Use the TI-83 Plus/TI-84 Plus calculator.

(a) Find the probability that x will be greater than 52. Round the final answer to at least four decimal places.

(b) Find the 35 percentile of x. Round the answer to at least two decimal places.

 

A sample of size 190 will be drawn from a population with mean 45 and standard deviation 11. Use the TI-83 Plus/TI-84 Plus calculator.

(a) Find the probability that x will be less than 43. Round the final answer to at least four decimal places.

(b) Find the 60 percentile of x. Round the answer to at least two decimal places.

 

Watch your cholesterol: The mean serum cholesterol level for U.S. adults was 201, with a standard deviation of 40.8 (the units are milligrams per deciliter). A simple random sample of 109 adults is chosen. Use Excel. Round the answers to at least four decimal places.

(a) What is the probability that the sample mean cholesterol level is greater than 208?

(b) What is the probability that the sample mean cholesterol level is between 193 and 199?

(c) Would it be unusual for the sample mean to be less than 195?

 

Taxes: The Internal Revenue Service reports that the mean federal income tax paid in the year 2010 was $8,040. Assume that the standard deviation is $5,000. The IRS plans to draw a sample of 1,000 tax returns to study the effect of a new tax law.

(a) What is the probability that the sample mean tax is less than $7,800? Round the answer to at least four decimal places.

(b) What is the probability that the sample mean tax is between $7,600 and $7,900? Round the answer to at least four decimal places.

(c) Find the 70 percentile of the sample mean. Round the answer to at least two decimal places.

(d) Would it be unusual if the sample mean were less than $7,900? Round the answer to at least four decimal places.

(e) Do you think it would be unusual for an individual to pay a tax of less than $7,900? Explain. Assume the variable is normally distributed. Round the answer to at least four decimal places.

 

High-rent district: The mean monthly rent for a one-bedroom apartment without a doorman in Manhattan is $2,676. Assume the standard deviation is $509. A real estate firm samples 108 apartments. Use Excel.

(a) What is the probability that the sample mean rent is greater than $2,746? Round the answer to at least four decimal places.

(b) What is the probability that the sample mean rent is between $2,550 and $2,555? Round the answer to at least four decimal places.

(c) Find the 75 percentile of the sample mean. Round the answer to at least two decimal places.

(d) Would it be unusual if the sample mean were greater than $2,780? Round the answer to at least four decimal places.

(e) Do you think it would be unusual for an individual apartment to have a rent greater than $2,780? Explain. Assume the population is approximately normal. Round the answer to at least four decimal places.

 

Annual income: The mean annual income for people in a certain city (in thousands of dollars) is 46, with a standard deviation of 34. A pollster draws a sample of 90 people to interview.

(a) What is the probability that the sample mean income is less than 41? Round the answer to at least four decimal places.

(b) What is the probability that the sample mean income is between 42 and 47? Round the answer to at least four decimal places.

(c) Find the 20 percentile of the sample mean. Round the answer to at least one decimal place.

(d) Would it be unusual for the sample mean to be less than 34? Round the answer to at least four decimal places.

(e) Do you think it would be unusual for an individual to have an income of less than 34? Explain. Assume the population is approximately normal. Round the answer to at least four decimal places.