Question

The grades on a statistics test are normally distributed with a mean of 62 and Q1=52. If the instructor wishes to assign B's or higher to the top 30% of the students in the class, what grade is required to get a B or higher?  

Please round your answer to two decimal places.

Answer 1

Solution:-
Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by

Z = (X-μ)/σ

Mean of 62, μ = 62
Q1 of 52 means that the z score of X = 52 has a pvalue of 0.25. Z has a pvalue of 0.25 between -0.67 and -0.68, so we use Z = -0.675

Z = (X-μ)/σ

-0.675 = (52 - 62)/σ
-0.675σ = -10
σ = -10/-0.675
σ = 14.8

If the instructor wishes to assign B's or higher to the top 30% of the students in the class, what grade is required to get a B or higher?

Those are the Z scores that have a pvalue higher than 0.70. So we have to find X when Z has a pvalue of 0.70. This is between 0.52 and 0.53, so we use Z = 0.525

Z = (X-μ)/σ
0.525 = (X - 62)/14.8
X = 62 + 0.525*0.525
X = 69.77

To get a B or higher, you need to get a grade of at least 69.77