Question

Scores of an IQ test have a​ bell-shaped distribution with a mean of 100 and a standard deviation of 17. What percentage of people has an in score between 83 and 117

Answer 1

To find the percentage of people with an IQ score between 83 and 117, we need to find the area under the bell-shaped curve between these two scores.

First, we need to standardize the scores by subtracting the mean from each score and dividing by the standard deviation.

For a score of 83:
Standardized score = (83 - 100) / 17 = -1

For a score of 117:
Standardized score = (117 - 100) / 17 = 1

Now, we can find the area under the curve between these standardized scores using a standard normal distribution table or calculator.

Using a standard normal distribution table, we can find the area for a standardized score of -1 as 0.1587. This represents the percentage of people below a score of 83.

Similarly, the area for a standardized score of 1 is 0.8413, representing the percentage of people below a score of 117.

To find the area between these two scores, we subtract the area below 83 from the area below 117:

0.8413 - 0.1587 = 0.6826

So approximately 68.26% of people have an IQ score between 83 and 117.