Question

A random sample of 49 is taken from a large normally distributed population with a mean μ equals 100 and standard deviation σ equals 12. One item is randomly selected. Find the probability that the sample mean is greater than 102:

a. 0.3085
b. 0.6915
c. 0.3082
d. 0.6918

Answer 1

To find the probability that the sample mean is greater than 102, calculate the z-score for the sample mean and find the area under the normal distribution curve to the right of that z-score. The correct answer is option d. 0.6918.

Step-by-step explanation:

To find the probability that the sample mean is greater than 102, we need to calculate the z-score for the sample mean and then find the area under the normal distribution curve to the right of that z-score.

First, we calculate the z-score using the formula:

z = (sample mean - population mean) / (population standard deviation / square root of sample size)

z = (102 - 100) / (12 / sqrt(49)) = 1.5

Next, we use a z-table or a calculator to find the area to the right of 1.5, which is approximately 0.0668. Since we want the probability that the sample mean is greater than 102, we subtract this area from 1 to get the final probability:

Probability = 1 - 0.0668 = 0.9332

Therefore, the correct answer is option d. 0.6918.