A grocery store's receipts show that sunday customer purchases have a skewed distribution with a mean of $3030 and a standard deviation of $2121. suppose the store had 304304 customers this sunday. a) estimate the probability that the store's revenues were at least $9 comma 6009,600. b) if, on a typical sunday, the store serves 304304 customers, how much does the store take in on the worst 11 % of such days?

Question

Turner Johnston

Mathematics

16 December, 04:31

A grocery store's receipts show that sunday customer purchases have a skewed distribution with a mean of $3030 and a standard deviation of $2121. suppose the store had 304304 customers this sunday. a) estimate the probability that the store's revenues were at least $9 comma 6009,600. b) if, on a typical sunday, the store serves 304304 customers, how much does the store take in on the worst 11 % of such days?

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Mason Yu · Answer 1

A. we use the z statistic to solve this problem

z = (x - u) / s

We calculate the value of the sample mean u and standard deviation s:

u = $30 * 304 = $9120

s = $21 * 304 = $6384

z = (9,600 - 9120) / 6384

z = 0.075

From the normal tables using right tailed test,

P = 0.47

B. At worst 11% means P = 0.11, so the z value at this is z = - 1.23

-1.23 = (x - 9120) / 6384

x = 1267.68