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Chapter 6: Q4 (page 281)

The accompanying histogram is constructed from the diastolic blood pressure measurements of the 147 women included in Data Set 1 “Body Data” in Appendix B. If you plan to conduct further statistical tests and there is a loose requirement of a normally distributed population, what do you conclude about the population distribution based on this histogram?

Short Answer

Expert verified

The population distribution is approximately normal.

Step by step solution

01

Given information

A sample is considered showing the diastolic blood pressure measurements of 147 women. The histogram of the 147 blood pressures is plotted.

02

Shape of a histogram for normal distribution

A histogram of the sample values can be plotted to check whether a sample comes from a normally distributed population.

If the histogram is bell-shaped, then the sample can be assumed to be from a normally distributed population, otherwise not.

Here, the histogram of the 147 blood pressure levels appears to be approximately bell-shaped.

Therefore, the population from which the sample is taken is approximately normally distributed.

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Most popular questions from this chapter

Quarters After 1964, quarters were manufactured so that their weights have a mean of5.67 g and a standard deviation of 0.06 g. Some vending machines are designed so that you canadjust the weights of quarters that are accepted. If many counterfeit coins are found, you cannarrow the range of acceptable weights with the effect that most counterfeit coins are rejectedalong with some legitimate quarters.

a. If you adjust your vending machines to accept weights between 5.60 g and 5.74 g, what percentage of legal quarters are rejected? Is that percentage too high?

b. If you adjust vending machines to accept all legal quarters except those with weights in the top 2.5% and the bottom 2.5%, what are the limits of the weights that are accepted?

Finding Bone Density Scores. In Exercises 37–40 assume that a randomly selected subject is given a bone density test. Bone density 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 bone density test score corresponding to the given information. Round results to two decimal places.

If bone density scores in the bottom 2% and the top 2% are used as cutoff points for levels that are too low or too high, find the two readings that are cutoff values.

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

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Females

22.7 in

1.0 in

Normal

For males, find P90, which is the length separating the bottom 90% from the top 10%.

In Exercises 7–10, use the same population of {4, 5, 9} that was used in Examples 2 and 5. As in Examples 2 and 5, assume that samples of size n = 2 are randomly selected with replacement.

Sampling Distribution of the Sample Standard Deviation For the following, round results to three decimal places.

a. Find the value of the population standard deviation

b. Table 6-2 describes the sampling distribution of the sample mean. Construct a similar table representing the sampling distribution of the sample standard deviation s. Then combine values of s that are the same, as in Table 6-3 (Hint: See Example 2 on page 258 for Tables 6-2 and 6-3, which describe the sampling distribution of the sample mean.)

c. Find the mean of the sampling distribution of the sample standard deviation. d. Based on the preceding results, is the sample standard deviation an unbiased estimator of the population standard deviation? Why or why not?

Standard Normal Distribution Identify the two requirements necessary for a normal distribution to be a standard normal distribution
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