Question

Suppose that the scores on a reading ability test are normally distributed with a mean of and a standard deviation of . What proportion of individuals score more than points on this test? Round your answer to at least four decimal places.

Answer 1

The proportion of individuals score at most 74 points on this test is 70%.

Explanation:

The complete question is:

Suppose that the scores on a reading ability test are normally distributed with a mean of 70 and a standard deviation of 8. What proportion of individuals score at most 74 points on this test? Round your answer to at least four decimal places.

Solution:

Let X represent the scores on a reading ability test.

It is provided that
`X\sim N(70,8^(2))`.

Compute the probability that an individuals score is at most 74 points on this test as follows:

`P(X\leq 74)=P((X-\mu)/(\sigma)\leq (74-70)/(8))`

`=P(Z<0.50)\\=0.69146\\\approx 0.70`

Thus, the proportion of individuals score at most 74 points on this test is 70%.