Question

The grades on the last art exam had a mean of 75%. assume the population of grades on art exams is known to be distributed normally, with a standard deviation of 7%. approximately what percent of student earn a score between 75% and 82%?

37.2%
84.1%
34.1%
50%

Answer 1

34.1%

Explanation:

Step 1: use the z formula for 75%

z = x - μ /σ

z=0.75-0.75 / 0.7 = 0

Step 2: Go to the probability table and find 0

.50000 = 50%

Step 3: use the z formula for 82% now

z = x - μ / σ

z = 0.82 - 0.75 / 0.7 = 1

Step 4: Go to the probability table and find 1

.84134= 84.13

Step 5: subtract the two to find a score between 75% and 82%?

84.13-.50=34.13

Answer 2

Determine the z-scores of the 75% and 82% by using the equation,
z-score = (data - mean) / standard deviation

z-score of 75%
z-score = (75 - 75)/(7)
= 0
This translates to a percentile of 50%

z-score of 82%
z-score = (82 - 75) / (7)
= 1
This translates to a percentile of 84.13%

To determine the answer to this item, we have to get the difference between the two percentiles. This gives us the answer of 34.13%.

Thus, the answer is the third choice.