# The Normal Distribution and Confidence Intervals

Basic Statistics

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Test 2- The Normal Distribution and Confidence Intervals

1) Assume that the distribution of heights of adult American men is normally distributed

with mean 69 inches and standard deviation 2.8 inches.

A Carefully label the x- and z-axes of the normal distribution.

B. What percentage of men is taller than 72.5 inches?

C. What is the probability of randomly selecting a man between the heights of 66 inches and 72.5 inches?

D. If only the tallest 2% of the male population are allowed to join an exclusive social club, what is the cutoff height.

2) Assume IQ scores are normally distributed with a population mean of 100 and a population standard deviation of 15. A random sample of 64 individuals are randomly selected from the population.

A. Carefully label the x-bar axis and z-axis of the sampling distribution for the samples of size 64.

B. What is the probability that the average IQ from a random sample of 64 individuals, is greater than 102?

C. What is the probability the average IQ, selected from a random sample of 64 individuals, is less than 94?

3) A certain company is concerned about its hiring policies. The job pool has been very large, with an equal number of equally qualified men and women. Over the last few years this company has hired 41 women out of the last 100 new employees. Assuming no discrimination based on gender, what is the probability of getting 41 or fewer women when 100 new employees are hired? Use the normal distribution to approximate the binomial distribution AND DON'T FORGET TO INVLUDE THE CONTINUITY CORRECTION.

4) Mileage tests were conducted on a randomly selected sample of 200 newly developed automobile tires. The average tread wear from this sample was found to be 50,000 miles with a standard deviation of 3,500 miles. Construct a 99% confidence interval for the population mean tread wear for this type of tire.

5) A survey of 15 grocery stores revealed that the average price of a gallon of milk was $2.98 with a standard deviation of $0.10. What is the 95% confidence interval to estimate the population mean cost of a gallon of milk?

6) Suppose 1,080 of 2,000 registered voters sampled said they are planning to vote for the Democratic candidate for president. Using the 0.95 degree of confidence, what is the interval estimate for the population proportion (to the nearest tenth of a percent)?

7) A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time students spent studying per week. Assuming a population standard deviation of 6 hours (acquired from previous surveys of years past), what is the required sample size if the error is to be less than 1/2 hour with a 95% level of confidence?

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#### Solution Summary

Step-by-step solutions are provided in the Word file attached. The normal distribution and confidence intervals are examined.