Question

I developed an achievement test and normalized it on people throughout the country over a year. My test has scores that are normally distributed with a mean of 100 and a standard deviation of 20. a. Find the probability that a randomly selected adult has IQ < 115 b. Find the probability that a randomly selected adult has IQ > 70 c. Find P30, which is the IQ score at the 30th percentile. d. What percentage of adults have scores between 80 and 120?

Answer 1

Here we have

(a)

The z-score for X = 115 is

The probability that a randomly selected adult has IQ < 115 is

Answer: 0.7734

(b)

The z-score for X = 70 is

The probability that a randomly selected adult has IQ > 70 is

Answer: 0.9332

(c)

Here we need z-score that has 0.30 area to its left. Using z table, z-score -0.52 has approximately 0.30 area to its left. So required X is

Answer: 89.6

(d)

The z-score for X = 80 is

The z-score for X = 120 is

The required percentage is