Question

The scores for math test #3 were normally distributed. If 15 students had a mean score of 74.8% and a standard deviation of 7.57, how many students scored above an 85%?

Answer 1

Answer: 1 student scored above an 85%.

Step-by-step explanation:

Let X = percentage score in test (normally distributed).

Given: Sample size = 15 , mean score : $\mu$= 74.8% = 0.748 ,standard deviation :  $\sigma=7.57$

Now, The probability that student scores above 85%:

$P(X>85)=P(\dfrac{X-\mu}{\sigma}>\dfrac{85-74.8}{7.57})\\\\=P(Z>1.347)\\\\=1-P(Z<1.347)\\\\=1-0.9110= 0.089$

Probability that student scores above 85% = 0.089

Number of students scored above an 85% = 0.089 x 15 = 1.335 ≈ 1

hence, 1 student scored above an 85%.