Question

A survey indicates that for each trip to a supermarket, a shopper spends an average of 41 minutes with a standard deviation of 12 minutes in the store. The lengths of time spent in the store are normally distributed and are represented by the variable x. When 200 shoppers enter the store, how many shoppers would you expect to be in the store for less than 30 minutes?

Answer 1

To find the number of shoppers in the store for less than 30 minutes, calculate the z-score and use a standard normal distribution table or calculator.

Step-by-step explanation:

To find the number of shoppers who would be in the store for less than 30 minutes, we need to calculate the z-score for the value 30 minutes. The z-score formula is z = (x - mean) / standard deviation.

Using the given information, the mean time spent in the store is 41 minutes and the standard deviation is 12 minutes. Plugging in these values, we get z = (30 - 41) / 12 = -0.9167.

We can then use a standard normal distribution table or calculator to find the probability associated with a z-score of -0.9167. This probability represents the percentage of shoppers who would be in the store for less than 30 minutes. Multiplying this probability by the total number of shoppers (200), we can estimate the number of shoppers in the store for less than 30 minutes.