Suppose that the scores on a reading ability test are normally distributed with a mean of 70 and a standard deviation of 9.

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 score at least 67points on this test? Round your answer to at least four decimal places.

Answer 1

To find the proportion of individuals who score at least 67 points on the reading ability test, we need to calculate the cumulative probability of the z-score corresponding to 67 points.

The z-score formula for the standard normal distribution is:

z = (X - μ) / σ

where:

X = The value we want to find the cumulative probability for (67 points in this case)

μ = Mean of the distribution (mean score on the test) = 70

σ = Standard deviation of the distribution = 9

Now, we can calculate the z-score:

z = (67 - 70) / 9

z = -0.3333 (approximate)

Next, we need to find the cumulative probability for this z-score, which represents the proportion of individuals scoring at least 67 points on the test. We can use a standard normal distribution table or a calculator to find this probability.

Using a calculator or a standard normal distribution table, the cumulative probability for z = -0.3333 is approximately 0.3707.

So, approximately 37.07% of individuals score at least 67 points on the reading ability test.