Question

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 between 95 and 105?

Answer 1

Answer: 0.9817

Step-by-step explanation:

Given : The Intelligence Quotient (IQ) test scores for adults are normally distributed with

Mean : $\mu=100$

Standard deviation : $\sigma=15$

Sample size : = 50

Let x be the random variable that represents the IQ test scores for adults.

Z-score : $z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

For x =95

$z=\dfrac{95-100}{\dfrac{15}{\sqrt{50}}}\approx-2.36$

For x =105

$z=\dfrac{105-100}{\dfrac{15}{\sqrt{50}}}\approx2.36$

By using standard normal distribution table , the probability the mean of the sample is between 95 and 105 :-

$P(95$