Question

A Statistics teacher decides to give A's only to students who score in the top 15% on the final exam.

The scores are normally distributed with a mean of 78 and a standard deviation of 7 (this is also the population standard deviation).

To the nearest integer value, what is the lowest score a student could earn and still receive an A? (Please show work)

A. 79

B. 80

C. 82

D. 83

E. 85

Answer 1

E. 85

Explanation:

We have been given that a Statistics teacher decides to give A's only to students who score in the top 15% on the final exam. The scores are normally distributed with a mean of 78 and a standard deviation of 7 (this is also the population standard deviation).

We will use normal distribution table and z-score formula to solve our given problem.

`z=(x-\mu)/(\sigma)`, where,

z= Z-score,

x = Sample score,

`\mu=\text{Mean}\\\sigma=\text{Standard deviation}`

`z=(x-78)/(7)`

We know that top 15% means 85% and more.

Let us find z-score corresponding to 85% or 0.85 using normal distribution table.

`1.04=(x-78)/(7)`

Let us solve for x.

`1.04*7=(x-78)/(7)*7`

`7.28=x-78`

`7.28+78=x-78+78`

`85.28=x`

`x\approx 85`

Therefore, the lowest score, a student could earn and still receive an A, is 85 and option E is the correct choice.