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

Answer:

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

Step-by-step 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:

$P(X\leq 74)=P(\frac{X-\mu}{\sigma}\leq \frac{74-70}{8})$

                 $=P(Z$

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