A popular retail store knows that the distribution of purchase amounts by its cu

Question

A popular retail store knows that the distribution of purchase amounts by its customers is approximately normal with a mean of $30 and a standard deviation of $9. Below you will find probability and percentile calculations related to the customer purchase amounts. a. What is the probability that a randomly selected customer will spend less than $15 at this store? b. What is the probability that a randomly selected customer will spend $20 or more at this store? c. What is the probability that a randomly selected customer will spend $30 or more at this store? d. What is the probability that a randomly selected customer will spend between $20 and $35 at this store? e. What two dollar amounts, equidistant from the mean of $30, such that 90% of all customer purchases are between these values? f. What two dollar amounts, equidistant from the mean of $30, such that 98% of all customer purchases are between these values?

Explanation / Answer

A) Required probability = 0.5000 + 0.3944 = 0.8944 ................... B) z value corresponding to X = $15........... z = (15 -25)/8 = - 1.25.............. Therefore the required probability = 0.3944 + 0.3944 = 0.7888

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