Question

A large company employs workers whose IQs are distributed normally with a mean of 95 and a standard deviation of 7.5. What percent of employees would have IQs less than 89%? The percentage of employees expected to have IQs less than 89% is _____%.

Answer 1

To determine the percentage of employees with IQs less than 89, calculate the z-score and then refer to a standard normal distribution table or software. Approximately 16% of the employees are expected to have an IQ of 89 or less.

Step-by-step explanation:

The percentage of employees expected to have IQs less than 89 can be determined using the properties of the normal distribution. We know the mean IQ is 95 and the standard deviation is 7.5. An IQ score of 89 is one standard deviation below the mean. To calculate the exact percentage, we would use the standard normal distribution or a z-score table. A z-score is calculated as (X - mean) / SD, which in this case would be (89 - 95) / 7.5.

After finding the z-score, you would look up this value in a standard normal distribution table or use software to find the percentage of employees with a score of 89 or lower. In a typical standard normal distribution, approximately 16% of values lie more than one standard deviation below the mean. Therefore, we would expect around 16% of the employees to have an IQ of 89 or less.