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Random Digits The digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9

Elementary Statistics | 12th Edition | ISBN: 9780321836960 | Authors: Mario F. Triola ISBN: 9780321836960 18

Solution for problem 5CRE Chapter 5.5

Elementary Statistics | 12th Edition

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Elementary Statistics | 12th Edition | ISBN: 9780321836960 | Authors: Mario F. Triola

Elementary Statistics | 12th Edition

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Problem 5CRE

Problem 5CRE

Random Digits The digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are randomly selected for applications including the selection of lottery numbers and the selection of telephone numbers to be called as part of a survey. In the following tables, the table at the left summarizes actual results from 100 randomly selected digits, and the table at the right summarizes the probabilities of the different digits.

Digit

Frequency

0

9

1

7

2

12

3

10

4

10

5

11

6

8

7

8

8

14

9

11

Digit x

P(x)

0

0.1

1

0.1

2

0.1

3

0.1

4

0.1

5

0.1

6

0.1

7

0.1

8

0.1

9

0.1

a. What is the table at the left called?

b. What is the table at the right called?

c. Use the table at the left to find the mean. Is the result a statistic or a parameter?

d. Use the table at the right to find the mean. Is the result a statistic or a parameter?

e. If you were to randomly generate 1000 such digits, would you expect the mean of these 1000 digits to be close to the result from part (c) or part (d)? Why?

Step-by-Step Solution:

Answer:

Step 1:

           Given that,The digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are randomly selected for applications including the selection of lottery numbers and the selection of telephone numbers to be called as part of a survey.

                 In the given tables, the table at the left summarizes actual results from 100 randomly selected digits, and the table at the right summarizes the probabilities of the different digits.

           

                               

                  Left table

          Right table

          Digit(x)

 Frequency(f)    

    Digit (x)

 P(x)

           0

       9

           0

   0.1

           1

       7

           1

   0.1

           2

       12

           2

   0.1

           3

       10

           3

   0.1

           4

       10

           4

   0.1

           5

       11

           5

   0.1

           6

        8

           6

   0.1

           7

        8

           7

   0.1

           8

       14

           8

   0.1

           9

        11

           9

   0.1

 

 Total = 1

      a).  It is called Frequency Distribution or Frequency Table because it shows the frequency of each digits.

      b). The second table is called a Probability Distribution table.

      c). The mean in the first table is given below:

         

         

   

                           Left table

      Digit (x)

 Frequency(f)    

fx  

           0

       9

0

           1

       7

7

           2

       12

24

           3

       10

30

           4

       10

40

           5

       11

55

           6

        8

48

           7

        8

56

Step 2 of 1

Chapter 5.5, Problem 5CRE is Solved
Textbook: Elementary Statistics
Edition: 12
Author: Mario F. Triola
ISBN: 9780321836960

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Random Digits The digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9