Question

Suppose that the scores on a reading ability test are normally distributed with a mean of 60 and a standard deviation of 10 . What proportion of individuals score less than 79 points on this test?

Answer 1

To find the proportion of individuals who score less than 79 points on the reading ability test, we need to calculate the cumulative probability for a z-score of 1.9.

Step-by-step explanation:

To find the proportion of individuals who score less than 79 points on the reading ability test, we need to find the area to the left of 79 under the normal distribution curve. We can calculate this using the z-score formula:

1. Calculate the z-score using the formula z = (x - mean) / standard deviation = (79 - 60) / 10 = 1.9.
2. Using a standard normal distribution table or a calculator, find the cumulative probability for a z-score of 1.9, which is approximately 0.9713.
3. Therefore, the proportion of individuals who score less than 79 points on the test is approximately 0.9713, or 97.13%.