Question

Suppose that the scores on a reading ability test are normally distributed with a mean of 70 and a standard deviation of 9. What proportion of individuals scores at least 55 points on this test? Round the answer as needed.

Answer 1

To find the proportion of individuals who score at least 55 points on the reading ability test, we calculate the area under the normal distribution curve to the right of 55.

Step-by-step explanation:

To find the proportion of individuals who score at least 55 points on the reading ability test, we need to calculate the area under the normal distribution curve to the right of 55.

First, we need to standardize the score of 55 using the z-score formula:

z = (x - mean) / standard deviation

Substituting the values, we get:

z = (55 - 70) / 9 = -1.67

Next, we need to find the area to the right of the z-score -1.67. We can use a standard normal distribution table or a calculator to find this area, which is approximately 0.9525.

Therefore, the proportion of individuals who score at least 55 points on the reading ability test is approximately 0.9525.