Suppose the time it takes for a purchasing agent to complete an online ordering process is normally distributed with a mean of 8 minutes and a standard deviation of 2
Minutes. Suppose a random sample of 25 ordering processes is selected. What is the
Probability that the sample mean will be less than 7.5 minutes?
A) 0.3944
B) 0.1056
C) 0.2114
D) 0.4013
E) 0.8944

Question

Quizplus · Accepted Answer

We need to calculate the z-score of the sample mean using the formula: z = (x̄ - μ) / (σ / √n), where x̄ is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size. Substituting the given values, we get: z = (7.5 - 8) / (2 / √25) = -1.25. Now we need to find the probability that the sample mean will be less than 7.5 minutes, which is equivalent to finding the probability that a standard normal random variable Z is less than -1.25. Consulting a standard normal table or using a calculator, we get: P(Z < -1.25) = 0.1056. Therefore, the answer is option B.

Suppose the Time It Takes for a Purchasing Agent to Complete