Question

Find the indicaled tQ score. The graph to the right depicts iQ scores of adults, and those sceres are normally distributed with a maan of 100 and a standard devalion of 15.

Answer 1

To find the probability that the sample mean scores will be between 85 and 125 points, we can use the concept of the normal distribution and z-scores. The z-scores for the lower and upper bounds can be calculated using the mean and standard deviation. Then, we can find the probability by finding the area between these two z-scores.

Step-by-step explanation:

To find the probability that the sample mean scores will be between 85 and 125 points, we can use the concept of the normal distribution. The mean IQ score is 100 and the standard deviation is 15. Since the sample size is large (20 adults), we can use the Central Limit Theorem to approximate the sample mean as a normal distribution. We can convert the raw scores to z-scores by subtracting the mean and dividing by the standard deviation. Then we can find the probability using the z-score table or a calculator.

The z-score for the lower bound (85) is calculated as follows: (85 - 100) / 15 = -1. The z-score for the upper bound (125) is calculated as follows: (125 - 100) / 15 = 1.67. The probability of the sample mean being between 85 and 125 can be found by finding the area between these two z-scores using the z-score table or a calculator.