Final answer:
The probability that the sample mean of 20 adults' IQ scores is between 85 and 125 can be calculated using z-scores and the Standard Normal Distribution. The calculation involves determining the z-scores for 85 and 125 and then finding the corresponding probabilities in a Z-Table.
Step-by-step explanation:
The question involves calculating the probability that the sample mean of IQ scores will fall between two given values. The IQ scores of a reference population distributed according to a normal distribution form the base for this probabilistic calculation. The method of calculating this involves using the standard normal distribution and z-scores, which are the number of standard deviations a score is from the mean.
To find the probability that the sample mean of 20 adults' IQ scores is between 85 and 125, we first need to determine the z-scores for 85 and 125 using the formula:
z = (X - μ) / (σ / √ n)
Where X is the score, μ is the population mean, σ is the population standard deviation, and n is the sample size. After finding the z-scores for both 85 and 125, we use a Z-Table of Standard Normal Distribution to find the probabilities corresponding to these z-scores. The difference between these probabilities will give us the probability that the sample mean is between 85 and 125. This process is central in statistics when dealing with the sampling distributions of means.