Question

Assume that adults have IQ scores that are normally distributed with a mean of mu equals 100 and a standard deviation sigma equals 20. Find the probability that a randomly selected adult has an IQ between 85 and 115.

Answer 1

Answer: 0.5467

Step-by-step explanation:

We assume that the test scores for adults are normally distributed with

Mean : $\mu=100$

Standard deviation : $\sigma=20$

Sample size : = 50

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

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

For x =85

$z=\dfrac{85-100}{20}\approx-0.75$

For x =115                                                                                                                                            

$z=\dfrac{115-100}{20}\approx0.75$

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

$P(85$

Hence, the probability that a randomly selected adult has an IQ between 85 and 115 =0.5467