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Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger
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Consider the lengths of stay at a hospital’s emergency

Chapter 3, Problem 111E

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QUESTION:

Problem 111E

Consider the lengths of stay at a hospital’s emergency department in Exercise 3-33. Assume that five persons independently arrive for service.

(a) What is the probability that the length of stay of exactly one person is less than or equal to 4 hours?

(b) What is the probability that exactly two people wait more than 4 hours?

(c) What is the probability that at least one person waits more than 4 hours?

3-33. Actual lenghts of stay at a hospitat’s emergency depament in 20009 are shown in the following table (rounded to the nearest hour. Length of stay is the total of wait and service times. Some longer stays are also approximated as 15 hours in this table.

Hours

Count

Percent

1

19

3.80

2

51

10.20

3

86

17.20

4

102

20.40

5

87

17.40

6

62

12.40

7

40

8.00

8

18

3.60

9

14

2.80

10

11

2.20

15

10

2.00

Calculate the probability mass function of the wait time for service.

Questions & Answers

QUESTION:

Problem 111E

Consider the lengths of stay at a hospital’s emergency department in Exercise 3-33. Assume that five persons independently arrive for service.

(a) What is the probability that the length of stay of exactly one person is less than or equal to 4 hours?

(b) What is the probability that exactly two people wait more than 4 hours?

(c) What is the probability that at least one person waits more than 4 hours?

3-33. Actual lenghts of stay at a hospitat’s emergency depament in 20009 are shown in the following table (rounded to the nearest hour. Length of stay is the total of wait and service times. Some longer stays are also approximated as 15 hours in this table.

Hours

Count

Percent

1

19

3.80

2

51

10.20

3

86

17.20

4

102

20.40

5

87

17.40

6

62

12.40

7

40

8.00

8

18

3.60

9

14

2.80

10

11

2.20

15

10

2.00

Calculate the probability mass function of the wait time for service.

ANSWER:

Solution:

Step 1 of 4:

    From the exercise 3-33.

Let us consider the lengths of stay at a hospital emergency department in 2009 are shown in the given table.  

Hours

Count

Percent

1

19

3.8

2

51

10.2

3

86

17.2

4

102

20.4

5

87

17.4

6

62

12.4

7

40

8

8

18

3.6

9

14

2.8

10

11

2.2

15

10

2

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