The amount of time that you have to wait before seeing the doctor in the doctor's office is normally distributed with a mean of 15.2 minutes and a standard deviation of 15.2 minutes.If you take a random sample of 35 patients,what is the probability that the average wait time is greater than 20 minutes? (Hint: Round the probability value to 2 decimal places. )
A)0.28
B)0.16
C)0.09
D)0.03

Question

Quizplus · Accepted Answer

To solve this problem, we need to use the central limit theorem which states that the sample mean follows a normal distribution with the mean equal to the population mean and the standard deviation equal to the population standard deviation divided by the square root of the sample size.

Using this, we can calculate the z-score as follows:

z = (x̄ - μ) / (σ / √n)
z = (20 - 15.2) / (15.2 / √35) 
z = 1.66

Using a standard normal distribution table, we find the probability of z being greater than 1.66 is 0.0475.

Therefore, the probability that the average wait time is greater than 20 minutes is 0.0475, which is approximately 0.03 when rounded to two decimal places. Hence, the correct answer is D.

The Amount of Time That You Have to Wait Before