Question: Your restaurant will serve 50 dinner groups tonight. Assume that the mean check size of dinner groups in general is $60, the standard deviation is

Your restaurant will serve 50 dinner groups tonight. Assume that the mean check size of dinner groups in general is $60, the standard deviation is $40, and the distribution is slightly skewed with a longer tail toward high values.
a. Find the mean and standard deviation for the total of all 50 checks.
b. Find the mean and standard deviation for the average of all 50 checks.
c. What further assumption is needed in order for you to conclude that the total of all 50 checks is approximately normally distributed?
d. Find the probability that the total of all 50 checks is more than $3,100, assuming a normal distribution.
e. Find the probability that the average of all 50 checks is between $58 and $65, assuming a normal distribution.

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