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Chapter 6: Q1 (page 291)

Bone Density Test.

In Exercises 1鈥�4, assume that scores on a bone mineral density test are normally distributed with a mean of 0 and a standard deviation of 1.

Bone Density Sketch a graph showing the shape of the distribution of bone density test scores.

Short Answer

Expert verified

The graph for the shape of distribution of bone density test scores is shown below:

Step by step solution

01

Given information

The bone mineral density test scores are normally distributed with mean value of 0 and standard deviation of 1.

02

Describe the random variable

Let Z be the random variable for bone mineral density test scores.

Z~N渭,蟽2~N0,12

The shape of the curve is expected to be bell-shaped, symmetric at mean value of 0.

03

Sketch the graph

The steps to sketch the graph are:

  1. Draw horizontal axis with values extending from 鈥�3 to 3 with a gap of 1 unit each.
  2. Sketch a bell shape curve such that it increases from 鈥�3 to 0 and then decreases smoothly from 0 to 3, maintaining symmetry at 0.

The graph is shown below:

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Most popular questions from this chapter

Critical Values. In Exercises 41鈥�44, find the indicated critical value. Round results to two decimal places.

z0.04

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.

Between -4.27 and 2.34

Standard normal distribution. In Exercise 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 score. If using technology instead of Table A-2, round answers to four decimal places.

Less than 2.56

Small Sample Weights of golden retriever dogs are normally distributed. Samples of weights of golden retriever dogs, each of size n = 15, are randomly collected and the sample means are found. Is it correct to conclude that the sample means cannot be treated as being from a normal distribution because the sample size is too small? Explain.

Water Taxi Safety Passengers died when a water taxi sank in Baltimore鈥檚 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 鈥淏ody Data鈥� 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?

b. If the water taxi is filled with 25 randomly selected men, what is the probability that their mean weight exceeds the value from part (a)?

c. After the water taxi sank, the weight assumptions were revised so that the new capacity became 20 passengers. If the water taxi is filled with 20 randomly selected men, what is the probability that their mean weight exceeds 175 lb, which is the maximum mean weight that does not cause the total load to exceed 3500 lb?

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