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06:36Fatal Car Crashes There are about 15,000 car crashes each day in the United States, and the proportion of car crashes that are fatal is 0.00559 (based on data from the National Highway Traffic Safety Administration). Assume that each day, 1000 car crashes are randomly selected and the proportion of fatal car crashes is recorded.
a. What do you know about the mean of the sample proportions?
College Presidents There are about 4200 college presidents in the United States, and they have annual incomes with a distribution that is skewed instead of being normal. Many different samples of 40 college presidents are randomly selected, and the mean annual income is computed for each sample.
a. What is the approximate shape of the distribution of the sample means (uniform, normal, skewed, other)?
Ergonomics. Exercises 9–16 involve applications to ergonomics, as described in the Chapter Problem.
Water Taxi Safety Passengers died when a water taxi sank in Baltimore’s Inner Harbor. Men are typically heavier than women and children, so when loading a water taxi, assume a worst-case scenario in which all passengers are men. Assume that weights of men are normally distributed with a mean of 189 lb and a standard deviation of 39 lb (based on Data Set 1 “Body Data” in Appendix B). The water taxi that sank had a stated capacity of 25 passengers, and the boat was rated for a load limit of 3500 lb.
a. Given that the water taxi that sank was rated for a load limit of 3500 lb, what is the maximum mean weight of the passengers if the boat is filled to the stated capacity of 25 passengers?
Ergonomics. Exercises 9–16 involve applications to ergonomics, as described in the Chapter Problem.
Designing Manholes According to the website www.torchmate.com, “manhole covers must be a minimum of 22 in. in diameter, but can be as much as 60 in. in diameter.” Assume that a manhole is constructed to have a circular opening with a diameter of 22 in. Men have shoulder widths that are normally distributed with a mean of 18.2 in. and a standard deviation of 1.0 in. (based on data from the National Health and Nutrition Examination Survey).
a. What percentage of men will fit into the manhole?
Sleepwalking Assume that 29.2% of people have sleepwalked (based on “Prevalence and Comorbidity of Nocturnal Wandering in the U.S. Adult General Population, by Ohayon et al., Neurology, Vol. 78, No. 20). Assume that in a random sample of 1480 adults, 455 have sleepwalked.
a. Assuming that the rate of 29.2% is correct, find the probability that 455 or more of the 1480 adults have sleepwalked.
Hershey Kisses Based on Data Set 38 “Candies” in Appendix B, weights of the chocolate in Hershey Kisses are normally distributed with a mean of 4.5338 g and a standard deviation of 0.1039 g.
a. What are the values of the mean and standard deviation after converting all weights of Hershey Kisses to z scores using z = (x - μ)/σ ?
b. The original weights are in grams. What are the units of the corresponding z scores?
