BackIn Exercises 8 and 9, assume that women have standing eye heights that are normally distributed with a mean of 59.7 in. and a standard deviation of 2.5 in. (based on anthropometric survey data from Gordon, Churchill, et al.).
a. If an eye recognition security system is positioned at a height that is uncomfortable for women with standing eye heights less than 54 in., what percentage of women will find that height uncomfortable?
Car Colors
In Exercises 9–12, assume that 100 cars are randomly selected. Refer to the accompanying graph, which shows the top car colors and the percentages of cars with those colors (based on PPG Industries).
Black Cars Find the probability that at least 25 cars are black. Is 25 a significantly high number of black cars?
Water Taxi Safety When a water taxi sank in Baltimore’s Inner Harbor, an investigation revealed that the safe passenger load for the water taxi was 3500 lb. It was also noted that the mean weight of a passenger was assumed to be 140 lb. Assume a “worst-case” scenario in which all of the passengers are adult men. Assume that weights of men are normally distributed with a mean of 188.6 lb and a standard deviation of 38.9 lb (based on Data Set 1 “Body Data” in Appendix B).
c. With a load limit of 3500 lb, how many male passengers are allowed if we assume the updated mean weight of 188.6 lb?
Small Sample Weights of M&M plain candies are normally distributed. Twelve M&M plain candies are randomly selected and weighed, and then the mean of this sample is calculated. Is it correct to conclude that the resulting sample mean cannot be considered to be a value from a normally distributed population because the sample size of 12 is too small? Explain.
Finding Area
In Exercises 23–36, find the indicated area under the standard normal curve. If convenient, use technology to find the area.
To the left of z=1.365
In Exercises 39 and 40, determine whether the finite correction factor should be used. If so, use it in your calculations when you find the probability.
Old Faithful In a sample of 100 eruptions of the Old Faithful geyser at Yellowstone National Park, the mean interval between eruptions was 129.58 minutes and the standard deviation was 108.54 minutes. A random sample of size 30 is selected from this population. What is the probability that the mean interval between eruptions is between 120 minutes and 140 minutes?
Find the area under the standard normal distribution to the left of a z-score of .
Find the area under the standard normal distribution to the right of a z-score of .
Find the area of the shaded region under the standard normal distribution.
Find the z-score such that (Z < z).
Find the z-score corresponding to the probability/area shown under the standard normal curve below.
Normal Distribution If the following data are randomly selected, which are expected to have a normal distribution?
a. Weights of Reese’s Peanut Butter Cups
Standard Normal Distribution. In Exercises 17–36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the probability of the given bone density test scores. If using technology instead of Table A-2, round answers to four decimal places.
Between 1.50 and 2.00
In Exercises 25–28, use these parameters (based on Data Set 1 “Body Data” in Appendix B):
Men’s heights are normally distributed with mean 68.6 in. and standard deviation 2.8 in.
Women’s heights are normally distributed with mean 63.7 in. and standard deviation 2.9 in.
If the Navy changes the height requirements so that all women are eligible except the shortest 3% and the tallest 3%, what are the new height requirements for women?
Normal Distribution If the following data are randomly selected, which are expected to have a normal distribution?
d. Exact volumes of Coke in 12 oz cans