Question

Exam grades: Scores on a stats final in a large class were normally distributed with a mean of 75 and a standard deviation of 8.

A) Find the 40th percentile of the scores.

B) Find the 65th percentile of the scores.

C) The instructor wants to give an A to the students whose scores were in the top 10% of the class. What is the minimum score needed to get an A?

*show by keystrokes, like Inr, units

Step 1

Let X be the score on the Stat exam. X follows normal distribution with mean μ = 75 and the standard deviation σ = 8.

*p ^{th} percentile:*

The *p ^{t}*

Step 2

A.

**The 40th percentile of the scores:**

Let x_{1} be the 40^{th} percentile of the scores. That is, the score separates 40% of the observations from the highest 60% of the observations.

The value of x_{1} can be found by the below equation,

Step 3

B.

**The 65th percentile of the scores:**

Let x2 be the 65th percentile of the scores. That is, the score separates 65% of the observations from the...

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