In given problem, suppose that a cost is imposed of an amount equal to the square of the number of additional hours of sleep. What is the expected cost? Explain.
Problem
According to an article in Travel and Leisure, every person in a small study of sleep during vacation was found to sleep longer than average during the first vacation night.1 Suppose that the number of additional hours slept in the first night of a vacation, over the person's average number slept per night, is given by the following probability distribution:
|
x
|
P(x)
|
|
0
|
0.01
|
|
1
|
0.09
|
|
2
|
0.30
|
|
3
|
0.20
|
|
4
|
0.20
|
|
5
|
0.10
|
|
6
|
0.10
|
a. Verify that P(x) is a probability distribution.
b. Find the cumulative distribution function.
c. Find the probability that at most four additional hours are slept.
d. Find the probability that at least two additional hours are slept per night.