A typical adult has an average IQ score of 105 with a standard deviation of 20. If 20 randomly selected adults are given an IQ test, what is the probability that the sample mean scores will be between 85 and 125 points?

Using the Central Limit Theorem, we can assume that the sample means will follow a normal distribution with a mean of 105 and a standard deviation of 20/sqrt(20) = 4.47. We can then find the z-scores for a sample mean of 85 and a sample mean of 125: z1 = (85-105)/4.47 = -4.47 z2 = (125-105)/4.47 = 4.47 Using a z-table or a calculator, we can find the probabilities associated with these z-scores: P(z < -4.47) = 0.0000044 P(z > 4.47) = 0.0000044 To find the probability of the sample mean scores being between 85 and 125, we can subtract these probabilities from 1: P(-4.47 < z < 4.47) = 1 - 0.0000044 - 0.0000044 = 0.9999912 Therefore, the probability that the sample mean scores will be between 85 and 125 points is \approx imately 0.9999912 or 99.99912%.