Question

Yoonie is a personnel manager in a large corporation. Each month she must review 16 of the employees. From past experience, she has found that the reviews take her approximately four hours each to do with a population standard deviation of 1.2 hours. Let Χ be the random variable representing the time it takes her to complete one review. Assume Χ is normally distributed. Let be the random variable representing the mean time to complete the 16 reviews. Assume that the 16 reviews represent a random set of reviews.

Q. Find the probability that a meant of a month's reviews take Yoonie more than 4.3 hours.

Please use the normal distribution appletLinks to an external site. and put your answer in decimal with 4 decimal places.

Answer 1

First, we need to calculate the standard error of the mean (SEM) using the formula:

SEM = σ / √n

Where σ is the population standard deviation (1.2 hours) and n is the number of reviews (16).

SEM = 1.2 / √16 = 1.2 / 4 = 0.3 hours

Next, we standardize the value 4.3 hours using the formula:

z = (X - μ) / SEM

Where X is the value we want to standardize (4.3 hours), μ is the mean time for one review (4 hours), and SEM is the standard error of the mean (0.3 hours).

z = (4.3 - 4) / 0.3 = 0.3 / 0.3 = 1

Now, using the normal distribution applet, we find the probability corresponding to z = 1, which is approximately 0.8413.

Therefore, the probability that the mean of a month's reviews takes Yoonie more than 4.3 hours is 0.8413 (rounded to 4 decimal places).