The Intelligence Quotient (IQ) test scores for adults are normally distributed with a mean of 100 and a standard deviation of 15. What is the probability we could select a sample of 50 adults and find the mean of this sample is less than 95?
A) 0.0091
B) 0.9818
C) 0.4909
D) 0.9544

Question

Quizplus · Accepted Answer

To solve this problem we use the central limit theorem. The sample mean follows a normal distribution with a mean of 100 and a standard deviation of 15/√50=2.12. We need to find the probability that the sample mean is less than 95.

Using the z-score formula: 
z = (sample mean - population mean) / (standard deviation / sqrt(sample size)) 
z = (95 - 100) / (15 / sqrt(50)) 
z = -2.36

Looking up the z-score in a standard normal distribution table, we find the probability to be 0.0091. Therefore, the answer is A.

The Intelligence Quotient (IQ) Test Scores for Adults Are Normally