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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

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 

check_circleAnswer
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.

pth percentile:

The pth percentile separates the lowest p% of the observations from the highest (100 - p)% of the observations. Where,1< p <99.

Step 2

A.

The 40th percentile of the scores:

Let x1 be the 40th percentile of the scores. That is, the score separates 40% of the observations from the highest 60% of the observations.

The value of x1 can be found by the below equation,

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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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