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Chapter 6: Q3CRE (page 226)

In Exercises 1-3, use the following recent annual salaries (in millions of dollars) for players on the N.Y. Knicks professional basketball team.

23.4, 22.5, 11.5 ,7.1 ,6.0 ,4.1 ,3.3, 2.8, 2.6, 1.7, 1.6 ,1.3, 0.9 ,0.9, 0.6.

NY Knicks Salaries Round each of the salaries to the nearest million dollars, then construct a dotplot. Do the values appear to be from a population having a normal distribution?

Short Answer

Expert verified

The dot plot is shown below:

The sample observations do not seem to be part of a normally distributed population.

Step by step solution

01

Rounding the salaries to the nearest million dollars

The salaries are rounded to nearest million dollars as follows:

23, 23, 12, 7, 6, 4, 3, 3, 3, 2, 2, 1, 1, 1, 1

02

Sketch a dot plot

Steps to construct a dot plot are:

1. Draw a line using real numbers .

2. Mark dots for each value on the line.

3. If the value repeats, mark the dot above the previous one.

The dot plot is shown below:

03

Determine normality

If the pattern described by a dot plot resembles an approximate bell shape, it implies the observations are taken from a normally distributed population. Otherwise, the distribution is non-normal. Thus, the dot plot shows that the distribution does not appear to follow a normal distribution.

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Most popular questions from this chapter

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

In Exercises 9–12, find the indicated IQ score and round to the nearest whole number. The graphs depict IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler IQ test).

Random Digits Computers are commonly used to randomly generate digits of telephone numbers to be called when conducting a survey. Can the methods of this section be used to find the probability that when one digit is randomly generated, it is less than 3? Why or why not? What is the probability of getting a digit less than 3?

In Exercises 5–8, find the area of the shaded region. The graphs depict IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler IQ test).

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?
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