M6 WPSA - Writing/Problem Solving Activity

#1) In a survey of men in the U.S. (ages 20 - 29), the mean height was 69.4 inches with a standard deviation of 2.9 inches.

A) What height represents the 90th percentile?

B) What height represents the first quartile?

#2) The length of time people age 20-24 years spend driving per day is 52 minutes, with population standard deviation of 2.2 minutes. Assume the time is normally distributed.

A) Use the "Normal Calculator" in StatCrunch to find the probability that a randomly selected person in this age range has a drive time greater than 53 minutes. Copy your results from StatCrunchinto your work/document.

B) Now consider a distribution of Sample Means. You randomly select a sample of 20 people in this age range. What is the mean of this distribution? What is the standard deviation of this distribution? Use the "Normal Calculator" in StatCrunch to find the probability that the mean of this sample of 20 people is greater than 53 minutes. After the computation with the normal calculator, click on Ctrl, Alt, Print Screen to capture your screen and paste it into your solution file.

C) Explain why the result from part A is greater than the result from part B.

#3) A survey of U.S. adults found that 69% of those who text on cell phones receive spam or unwanted messages. You randomly select 100 U.S. adults who text on cell phones.

A) Determine whether you can use a normal distribution to approximate the binomial distribution.

B) Find the probability that the number who receive spam or unwanted messages is exactly 70.

C) Find the probability that the number who receivespamor unwanted messages is at least 70.

D) Find the probability that the number who receivespamor unwanted messages is fewer than 70.

E) Would any of the events in B through D be considered unusual? Justify your answer.