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Chapter 2: Q10 (page 48)

Normal Distributions. In Exercises 9 and 10, using a loose interpretation of the criteria for determining whether a frequency distribution is approximately a normal distribution, determine whether the given frequency distribution is approximately a normal distribution. Give a brief explanation.

Best Actors Refer to the frequency distribution from Exercise 6

Short Answer

Expert verified

As the frequencies begin from a small value, attain a peak, and then continue to decline and appear to be symmetric, it can be said that the given frequency distribution follows the normal distribution.

Step by step solution

01

Given information

Data are given on the ages of the best actors when they won the Oscar.

02

Normal distribution

A frequency distribution is considered to follow the normal distribution if the frequencies gradually increase from a small value, achieve a maximum value, and then the frequencies gradually decline.

Also, the frequencies on either side of the peak value should appear to be symmetric.

Here, the following frequency distribution is considered:

Age (years) of the best actors when the Oscar was won

Frequency

20-29

1

30-39

28

40-49

36

50-59

15

60-69

6

70-79

1

It can be observed that the frequencies start from a low value, reach the highest value of 36,and then continue to decrease eventually.

Also, the gradual rise of values before the maximum value and the gradual decline of the values after the maximum value appear to be symmetric.

Therefore, the frequency distribution of the ages of the best actors is normally distributed.

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Most popular questions from this chapter

Information provided by the World Meteorological Association revealed following data on the highest recorded temperature for each continent.

a. What type of data is presented in the first column of the table ?

b. What type of data is presented in the second column of the table ?

c. What type of data is presented in the third column of the table ?

d. What type of data is provided by the information that Death Valley is in the United States?

Categorical Data. In Exercises 23 and 24, use the given categorical data to construct the relative frequency distribution.

Births Natural births randomly selected from four hospitals in New York State occurred on the days of the week (in the order of Monday through Sunday) with these frequencies: 52, 66, 72, 57, 57, 43, 53. Does it appear that such births occur on the days of the week with equal frequency?

McDonald鈥檚 dinner service times refer to the accompanying table summarizing service times (seconds) of McDonald鈥檚 dinners. How many individuals are included in the summary? Is it possible to identify the exact values of all of the original service times?

Table for Exercise 1

McDonald鈥檚 Dinner Service Times

Times (sec)

Frequency

60-119

7

120-179

22

180-239

14

240-299

2

300-359

5

Frequency Polygon. In Exercises 15 and 16, construct the frequency polygons.

Tornadoes Use the frequency distribution from Exercise 12 in Section 2-1 on page 49 to construct a frequency polygon. Does the graph suggest that the distribution is skewed? If so, how?

Relative frequency distribution use percentages to construct the relative frequency distribution corresponding to the accompanying frequency distribution for McDonald鈥檚 dinner service times.
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