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Chapter 6: Q1CQQ (page 226)

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.

\(\begin{aligned}{c}Z \sim N\left( {\mu ,{\sigma ^2}} \right)\\ \sim N\left( {0,{1^2}} \right)\end{aligned}\)

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

Body Temperatures Based on the sample results in Data Set 3 鈥淏ody Temperatures鈥� in Appendix B, assume that human body temperatures are normally distributed with a mean of 98.20掳F and a standard deviation of 0.62掳F.

a. According to emedicinehealth.com, a body temperature of 100.4掳F or above is considered to be a fever. What percentage of normal and healthy persons would be considered to have a fever? Does this percentage suggest that a cutoff of 100.4掳F is appropriate?

b. Physicians want to select a minimum temperature for requiring further medical tests. What should that temperature be, if we want only 2.0% of healthy people to exceed it? (Such a result is a false positive, meaning that the test result is positive, but the subject is not really sick.)

SAT and ACT Tests Because they enable efficient procedures for evaluating answers, multiple choice questions are commonly used on standardized tests, such as the SAT or ACT.

Such questions typically have five choices, one of which is correct. Assume that you must make random guesses for two such questions. Assume that both questions have correct answers of 鈥渁.鈥�

a. After listing the 25 different possible samples, find the proportion of correct answers in each sample, then construct a table that describes the sampling distribution of the sample proportions of correct responses.

b. Find the mean of the sampling distribution of the sample proportion.

c. Is the mean of the sampling distribution [from part (b)] equal to the population proportion of correct responses? Does the mean of the sampling distribution of proportions always equal the population proportion?

Finding Bone Density Scores. In Exercises 37鈥�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.

Find P10, the 10th percentile. This is the bone density score separating the bottom 10% from the top 90%.

Standard Normal DistributionIn Exercises 17鈥�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 -2.75 and -0.75.

Continuous Uniform Distribution. In Exercises 5鈥�8, refer to the continuous uniform distribution depicted in Figure 6-2 and described in Example 1. Assume that a passenger is randomly selected, and find the probability that the waiting time is within the given range.

Between 2 minutes and 3 minutes
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