Question

Jan's All You Can Eat Restaurant charges ​$9.00 per customer to eat at the restaurant. Restaurant management finds that its expense per​ customer, based on how much the customer eats and the expense of​ labor, has a distribution that is skewed to the right with a mean of $8.20 and a standard deviation of $4. Complete parts​ (a) and​ (b).

a. If the 100 customers on a particular day have the characteristics of a random sample from their customer​ base, find the mean and standard deviation of the sampling distribution of the​ restaurant's sample mean expense per customer.

The mean is ___ . ​(Round to the nearest hundredth as​ needed.)

The standard deviation is ____ . ​(Round to the nearest hundredth as​ needed.)

b. Find the probability that the restaurant makes a profit that​ day, with the sample mean expense being less than ​$9.00.

​(Hint: Apply the central limit theorem to the sampling distribution in​ (a).)

Answer 1