Question

The AP Statistics Exam, like all other AP Exams, is graded on a 5, 4, 3, 2, 1, 0 basis. Many colleges require a 4 or a 5 to grant credit. In 1999, 25,240 students took the exam, and 30.4% of these received either a 4 or a 5. Assume that the raw scores were approximately normally distributed with a mean of 60 and a standard deviation of 19. What is the minimum score a student must receive to earn a 4 or a 5?

A.70
B.71
C.72
D.69
E.68

Answer 1

A minimum score of 70 is required for a student to earn a 4 or a 5.

Explanation:

We are given the following information in the question:

Mean, μ = 60

Standard Deviation, σ = 19

We are given that the distribution of raw scores is a bell shaped distribution that is a normal distribution.

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

Top 30.4% students received either a 4 or a 5. Let x denotes the score that separates top 30.4% students from lowest 69.6% students

We have to find the value of x such that the probability is 0.304

P(X > x)

`P( X > x) = P( z > \displaystyle(x - 60)/(19))=0.304`

`= 1 -P( z \leq \displaystyle(x - 60)/(19))=0.304`

`=P( z \leq \displaystyle(x - 60)/(19))=0.696`

Calculation the value from standard normal z table, we have,

`P(z<0.513) = 0.696`

`\displaystyle(x - 60)/(19) = 0.513\\x = 69.747 \approx 70`

A minimum score of 70 is required for a student to earn a 4 or a 5.