Answer:
the variance of the refund payment to the couple = 9463.394
Step-by-step explanation:
Given that :
A couple book a cruise to Alaska that promises to refund 100 per day of rain on the seven day cruise up to a maximum of 300.
It is possible that the couple won't be able to refund up 100 per day or more than 100 per day.
SO; let assume that the refund payment happens to be 0, 100,200, 300
Let X be the total refund payment on the seven day cruise.
We can say X = 0, if there is no rain on all 7 days.
If it rains on any one day; then X = 100
if it rains on any two day ; then X = 200
if it rains on any three day or more than that ; then X = 300
Now; we have our probability distribution function as:
P(X = 0) = 0.2097152
P(X = 100) = 0.3670016
P(X = 200) = 0.2752512
P(X = 300) = 0.148032
In order to determine the variance of the refund payment to the couple; we use the formula:
variance of the refund payment to the couple
where;
NOW;
the variance of the refund payment to the couple = 28002.944 - 18539.55
the variance of the refund payment to the couple = 9463.394
