Question

The distribution of scores on the Waichsler Adult Intelligence Scale (WAIS) for persons over 16 years of age is approximately normal with mean 100 and standard deviation 15.

A) What is the probability that a randomly chosen individual has a WAIS score of 105 or higher?

B) What is the probability that the average WAIS score of an SRS of 50 people is 105 or higher?

C) Would your answers to either (A) or (B) be affected if the distribution of WAIS scores in the population were distinctly non-normal?

Answer 1

A) P(X > 105)

= P((X - )/> (105 - )/)

= P(Z > (105 - 100)/15)

= P(Z > 0.33)

= 1 - P(Z < 0.33)

= 1 - 0.6293

= 0.3707

B) P(> 105)

= P(( - )/() > (105 - )/())

= P(Z > (105 - 100)/(15/))

= P(Z > 2.36)

= 1 - P(Z < 2.36)

= 1 - 0.9909

= 0.0091

C) Since the sample size in part B is greater than 30, so the sampling distribution of will be approximately normally distributed. So if the population is non-normal, so it will not affect the answer in part B. But it will affect the answer in part A.