Final answer:
The student's question involves calculating probabilities for the sample mean IQ from a normally distributed adult population with a mean of 123 and standard deviation of 20. The distribution of the sample mean is also normal, and probabilities can be calculated using z-scores and standard normal distribution tables.
Step-by-step explanation:
To address the student's question, we need to apply the concepts of normal distribution and sampling distributions. The student is provided with a mean IQ of 123 and a standard deviation of 20 in a large population of adults. When a sample of 60 adults is selected:
- (a) The distribution of IQ in the large population is normally distributed with a mean (μ) of 123 and a standard deviation (σ) of 20.
- (b) The distribution of the sample mean IQ is also normally distributed (by the Central Limit Theorem, given the sample size is large), with a mean (μ) of 123 and a standard deviation (σ/√n), which is 20/√60.
- (c) The probability that the sample mean IQ is less than 120 can be found using the standard normal distribution (z-scores). The z-score is calculated as (X- μ)/(σ/√n).
- (d) The probability that the sample mean IQ is greater than 120 is the complement of part (c), which can be found as 1 - P(X < 120).
- (e) The probability that the sample mean IQ is between 120 and 129 can be determined by calculating the probabilities for P(X < 129) and P(X < 120) and subtracting the two.
While we aren't provided with enough information to calculate these probabilities directly, this approach outlines how the student can use statistical methods to find the desired probabilities.