Astatistics 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? ( show work)

a. 79

b. 80

c. 82

d. 83

e. 85

E. 85

Step-by-step 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.

, where,

z= Z-score,

x = Sample score,

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

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

Let us solve for x.

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