Question

Suppose that your statistics professor tells you that the scores on a midterm exam were approximately

normally distributed with a mean of 78 and a standard deviation of 7. The top 15% of all scores have
been designated A’s. Your score is 89. Did you earn an A? Explain.

Answer 1

• Yes

Explanation:

z-score representing 85% is 1.04 (from table)

Let x be the score representing the lower limit of 85%.

Use the formula to find z-scores:

• z = (x - μ)/σ

We have:

• z = 1.04, μ = 78, σ = 7

Substitute the values and solve for x:

• 1.04 = (x - 78)/7
• x - 78 = 7.28
• x = 85.28

The lower limit of the top 15% is 85.28.

Since your score is greater than 85.28 you earned an A