(Problem 3) Human heights are known to be normally distributed.Men have a mean height of 70 inches and females a mean height of 64 inches.Both have a population standard deviation of 3 inches.

(3 points each, 15 points total)

(a) Find the 1^st Quartile (Q1) of the female height distribution

(b) Find the height of a female in the 90^th percentile

(c) What is the probability that a randomly selected female is above 70 inches height?

Assume a random sample of 100 males is selected.

(d) What is the standard deviation of the sample mean (also known as the standard error of the mean)?

(e) What is the probability that the mean height of samples is less than 68 inches tall?

HINT: Since we know the population standard deviation, you will always use the Normal Distribution

(Problem 4) The average height of students has a normal distribution with a standard deviation of 2.5 inches.You want to estimate the mean height of students at your college to within 1-inch with 95% confidence.How many students should you measure?HINT:Be sure to consider the two-tail probability when evaluating the z-score for the confidence level.See Illowsky, Chapter 8, Page 427

(10 points)

(Problem 5) A random sample of 100 test scores has a sample mean of 85.Assume that the test scores have a population standard deviation of 10. Construct a 95% confidence interval estimate of the mean test scores. HINT:See the Illowsky textbook, Section 8.1. (10 points)