A ski resort claims that there is a 75 percent chance of snow on any given day in January and that snowfall happens independently from one day to the next. A family plans a four-day trip to this ski resort in January. Let cap x represent the number of days it snows while the family is there. What are the mean and standard deviation of cap x ?
Answer
A
mu sub x is equal to 3 comma sigma sub x is equal to 0 point 7 5
B
mu sub x is equal to 1 comma sigma sub x is equal to 1
C
mu sub x is equal to 2 comma sigma sub x is equal to 0 point 5 6
D
mu sub x is equal to 3 comma sigma sub x is equal to 0 point 8 7
Explanation
The number of snowy days follows a binomial distribution with 4 days and a 0.75 chance of snow each day. Its mean is np = 4(0.75) = 3 days. Its standard deviation is √[np(1 − p)] = √[4(0.75)(0.25)] = √0.75 ≈ 0.87 days, so the mean is 3 and the standard deviation is 0.87.
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