Question

The wait times for the telephone help line at a computer company are normally distributed with a mean of

14 minutes and a standard deviation of 4 minutes.
1. If Marco calls the help line, what is the probability that his call will be answered in less than 9 minutes?
2. If Sophia calls the help line, what is the probability that she will have to wait over 17 minutes for her
call to be answered?

Answer 1

To find the probability for Marco's call, calculate the z-score using the formula. The probability is approximately 0.1056. To find the probability for Sophia's call, calculate the z-score using the formula. The probability is approximately 0.7734.

Step-by-step explanation:

To answer the first question, we need to calculate the z-score for Marco's call. The z-score formula is given by (x - mean) / standard deviation, where x is the value we want to find the probability for. In this case, x = 9, mean = 14, and standard deviation = 4.

Substituting the values into the formula, we get (9 - 14) / 4 = -1.25. We can then look up the probability corresponding to this z-score in the z-table or use a calculator to find that the probability is approximately 0.1056.

To answer the second question, we use the same process but with different values. Here, x = 17, mean = 14, and standard deviation = 4. Calculating the z-score, we get (17 - 14) / 4 = 0.75. The probability corresponding to this z-score is approximately 0.7734.