I have the following homework question. I also included the work done. Please advise if I am on the right track Thank you!!

"A recent study determined that the distance employees at a pharmaceutical company in New Jersey commute to work each way is normally distributed with a mean equal to 13.4 miles and a standard deviation of 3.6 miles. Management has decided to give a year-end bonus to employees who commute large distances and have decided to give the bonus to any employee who commutes over 18.7 miles. Based on this information, approximately 13.3 percent of the employees will get the year-end bonus.

Consider this situation and respond as to whether you agree with Management's conclusion that 13.3 percent of the employees will get the year-end bonus. Provide your rationale if you disagree with Management and provide the correct percent."

WORK DONE :

z(18.7) = (18.7-13.4)/3.6 = 1.5143&nbsp

P(x > 18.7) = P(z > 1.5143) = 0.0650 or 6.5%

Close. I get Z = 1.47, P = .0708 = 7.08%

so only 7.08 % of employees would be entitled to the bonus?

Based on the work you have shown, you are on the right track. However, there is a small mistake in the calculation of the probability.

To find the probability of an employee commuting over 18.7 miles, you correctly calculated the z-score:
z(18.7) = (18.7 - 13.4) / 3.6 = 1.5143

However, to find the probability P(x > 18.7), you need to look up the value in the standard normal distribution table.

From the z-score of 1.5143, you can look up the corresponding probability in the table. The table will give you the area to the left of the z-score. Since we are interested in the area to the right of the z-score (x > 18.7), you need to subtract the table value from 1 to get the correct probability.

Let's look up the z-score of 1.5143 in the table:
P(z > 1.5143) = 1 - P(z < 1.5143)

By looking up the z-score in the standard normal distribution table, you will find that P(z < 1.5143) is approximately 0.9350.

Therefore, P(x > 18.7) = 1 - P(z < 1.5143) = 1 - 0.9350 = 0.0650 or 6.5%.

So your calculation of 6.5% is correct. Based on the given information, approximately 6.5% of the employees will get the year-end bonus. This is different from the management's conclusion of 13.3%, so you would disagree with their conclusion.