Based on past experience, the number of customers who arrive at a local gasoline station during the noon hour to purchase fuel is best described by the probability distribution given in the file S04_41.xlsx.
a. Find the mean, variance, and standard deviation of this random variable.
b. Find the probability that the number of arrivals during the noon hour will be within one standard deviation of the mean number of arrivals.
c. Suppose that the typical customer spends $28 on fuel upon stopping at this gasoline station during the noon hour. Find the mean and standard deviation of the total gasoline revenue earned by this gas station during the noon hour.
d. What is the probability that the total gasoline revenue will be less than the mean value found in part c?
e. What is the probability that the total gasoline revenue will be more than two standard deviations above the mean value found in part c?