Question

(CO 3) A survey indicates that shoppers spend an average of 22 minutes with a standard deviation of 8 minutes in your store and that these times are normally distributed. Find the probability that a randomly selected shopper will spend less than 20 minutes in the store. 0.40 0.50 0.60 0.22

Answer 1

To calculate the probability of a shopper spending less than 20 minutes in the store, the Z-score is found using the formula Z = (X - μ) / σ, resulting in a Z-score of -0.25, which corresponds to a probability of approximately 0.40.

Step-by-step explanation:

The question asks for the probability that a randomly selected shopper will spend less than 20 minutes in a store, given that the average time spent is 22 minutes with a standard deviation of 8 minutes, and that these times are normally distributed. To find this probability, we use the Z-score formula:

Z = (X - μ) / σ

Where X is the value we are checking (20 minutes), μ is the mean (22 minutes), and σ is the standard deviation (8 minutes). Plugging in the numbers, we get:

Z = (20 - 22) / 8 = -0.25

Next, we look up the Z-score in a standard normal distribution table, or use a calculator with normal distribution functions, to find the probability that a Z-score is less than -0.25. This probability is approximately 0.40.