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Actual lengths of stay at a hospital’s emergency
Chapter 3, Problem 33E(choose chapter or problem)
Actual lengths of stay at a hospital’s emergency department in 2009 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:
Actual lengths of stay at a hospital’s emergency department in 2009 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:
Step 1 of 2
(a)
We have given the length of stay is the total of wait and service times.
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 |
We are asked to find the probability mass function (PMF) of the wait time for service.
The probability mass function (PMF) of a discrete random variable is the function
The probability mass function is sometimes called the probability distribution.
Let represent the wait time for service.
Hence the range can take values from the table,