Question

A survey indicates that for each trip to the Target store, a shopper spends an average of 25 minutes with a standard deviation of 14 minutes in the store. The length of time spent in the store is normally distributed and is represented by the variable x. A shopper enters the store. Find the probability that the shopper will be in the store for between 25 and 50 minutes. Probability that the shopper will be in the store for between 25 and 50 minutes. P = _________ Find the probability that the shopper will be in the store less than 25 minutes. distribution P = _________ Find the probability that the shopper will be in the store more than 30 minutes. distribution. P = _________ If 200 shoppers enter the store, how many shoppers would you expect to be in the store more than 40 minutes? Shoppers = _________

Answer 1

Solution:

We are given:

Find the probability that the shopper will be in the store for between 25 and 50 minutes

Answer: It is required to find:

Now using the z-score formula, we have:

  

  

Now using the standard normal table, we have:

Find the probability that the shopper will be in the store less than 25 minutes

Answer: We are required to find:

Using the z-score formula, we have:

Now using the standard normal table, we have:

Find the probability that the shopper will be in the store more than 30 minutes. distribution.

Answer: We are required to find:

Using the z-score formula, we have:

Now using the standard normal table, we have:

If 200 shoppers enter the store, how many shoppers would you expect to be in the store more than 40 minutes?

Answer: We will first find:

  

Using the z-score formula, we have:

Now using the standard normal table, we have:

Therefore, the number of shoppers that would be expected to be in the store for more than 40 minutes is:

The probability that the shopper will be in the store for between 25 and 50 minutes. P = 0.4629

The probability that the shopper will be in the store less than 25 minutes. distribution P = 0.5000

The probability that the shopper will be in the store more than 30 minutes. distribution. P = 0.3605

If 200 shoppers enter the store, how many shoppers would you expect to be in the store more than 40 minutes? Shoppers = 28