Question

The probability that a randomly selected adult has an IQ between 94 and 116 is (Type an integer or decimal rounded to four decimal places as needed.)

Answer 1

To find the probability that a sample mean of IQ scores will be between 85 and 125 points, we can use the Central Limit Theorem.

Step-by-step explanation:

To find the probability that a sample mean of IQ scores will be between 85 and 125 points, we can use the Central Limit Theorem. This theorem states that the distribution of sample means will be approximately normal, regardless of the shape of the population distribution, as long as the sample size is sufficiently large.

Given that the mean IQ score is 105 and the standard deviation is 20, we can calculate the z-scores for the lower and upper bounds: Lower z-score = (85 - 105) / (20 / sqrt(20)) = -1.5 Upper z-score = (125 - 105) / (20 / sqrt(20)) = 1.5

Using a z-score table or a calculator, we can find the area under the normal curve between these z-scores. The probability that the sample mean scores will be between 85 and 125 points is the difference between these two areas.