The Intelligence Quotient (IQ)test scores for adults are normally distributed with a population mean of 100 and a population 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 need to use the formula for the distribution of the sample mean:

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.

In this case, we want to find the probability that a sample of 50 adults will have a mean IQ score less than 95. So, we plug in the given values:

z = (95 - 100) / (15 / √50)

z = -2.89

To find the probability associated with this z-score, we consult a standard normal distribution table (or use a calculator). The probability of getting a z-score less than -2.89 is approximately 0.0091.

Therefore, the answer is choice A: 0.0091.

The Intelligence Quotient (IQ)test Scores for Adults Are Normally Distributed