Question

A grocery store's receipts show that Sunday customer purchases have a skewed distribution with a mean of $32 and a standard deviation of $23. Suppose the store had 100 customers this Sunday. a) Estimate the probability that the store's revenues were at least $_____. b) If, on a typical Sunday, the store serves 200 customers, how much does the store take in on the worst _____% of such days?

Answer 1

To estimate the probability of the store's revenues and find the revenue on the worst x% of days, we need to calculate the z-score using the mean and standard deviation.

Step-by-step explanation:

To estimate the probability of the store's revenues being at least a certain amount, we need to find the z-score associated with that amount. The formula for the z-score is z = (X - μ) / σ, where X is the desired revenue, μ is the mean, and σ is the standard deviation. Once we have the z-score, we can use a standard normal distribution table or calculator to find the corresponding probability.

To find the revenue on the worst x% of days, we need to find the z-score associated with the x% percentile of the distribution. The formula for the z-score in this case is z = InvNorm(x/100, μ, σ), where InvNorm is the inverse of the cumulative distribution function of the normal distribution. Once we have the z-score, we can calculate the revenue using the formula X = z * σ + μ.