Question

Suppose that a large Introduction to Psychology class has taken a midterm exam, and the scores are normally distributed with a mean of 75 and a standard deviation of 9.

a. What proportion of the class got scores above 90?

b. What percent of the class got scores below 78?

c. What percent of the class got scores above 68?

d. What proportion of the class got scores below 94?

Answer 1

Solution: We are given:

a. What proportion of the class got scores above 90?

Answer: We are required to find:

Using the z-score formula, we have:

  

Now using the standard normal table, we have:

Therefore, the proportion of the class that got scores above 90 is 0.0478

b. What percent of the class got scores below 78?

Answer: We are required to find:

Using the z-score formula, we have:

  

Now using the standard normal table, we have:

Therefore, the percent of the class that got scores below 78 is 63.04%

c. What percent of the class got scores above 68?

Answer: We are required to find:

Using the z-score formula, we have:

  

Now using the standard normal table, we have:

Therefore, the percent of the class that got scores above 68 is 78.17%

d. What proportion of the class got scores below 94?

Answer: We are required to find:

Using the z-score formula, we have:

  

Now using the standard normal table, we have:

Therefore, the proportion of the class that got scores below 94 is 0.9826