Chapter 6: Q6.15 (page 260)
A variable is approximately normally distributed. If you draw a histogram of the distribution of the variable, roughly what shape will it have ?
The histogram of a Normal Distribution is Bell Shaped.
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In Exercises 13–20, use the data in the table below for sitting adult males and females (based on anthropometric survey data from Gordon, Churchill, et al.). These data are used often in the design of different seats, including aircraft seats, train seats, theater seats, and classroom seats. (Hint: Draw a graph in each case.)
Mean | St.Dev. | Distribution | |
Males | 23.5 in | 1.1 in | Normal |
Females | 22.7 in | 1.0 in | Normal |
For males, find , which is the length separating the bottom 90% from the top 10%.
Normal Distribution What’s wrong with the following statement? “Because the digits 0, 1, 2, . . . , 9 are the normal results from lottery drawings, such randomly selected numbers have a normal distribution.”
Standard normal distribution, 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 score. If using technology instead of Table A-2, round answers to four decimal places.
Greater than 0
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)?
b. What value do the sample means target? That is, what is the mean of all such sample means?
Durations of PregnanciesThe lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days.
a. In a letter to “Dear Abby,” a wife claimed to have given birth 308 days after a brief visit fromher husband, who was working in another country. Find the probability of a pregnancy lasting308 days or longer. What does the result suggest?
b. If we stipulate that a baby is prematureif the duration of pregnancy is in the lowest 3%,find the duration that separates premature babies from those who are not premature. Premature babies often require special care, and this result could be helpful to hospital administrators in planning for that care.
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