Question

The results on a statistics quiz are normally distributed with a mean of 74 and a standard deviation of 8.

Find (a) the lowest passing grade if the lowest 20% of the students are given F’s. x1 = , round your answer to the nearest whole number

(b) the highest B if the top 8 % of the students are given A’s. x2 = , round your answer to the nearest whole number.

Answer 1

a) x1 = 67

b) x2 = 85

Explanation:

mean ( )= 74,  standard deviation ( )= 8.

a)

the lowest passing grade if the lowest 20% of the students are given F’s

We want to find 20th percentile

now using normal z table find z-score for 0.20 we get,

z-score = -0.8416

formula is

x = 74 + ( -0.8416 * 8)

x = 67.2672

rounding to nearest whole number

x1 = 67

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b)

the highest B if the top 8 % of the students are given A’s.

We ant to find 92th percentile hence,

now using normal z table find z-score for 0.92 we get,

z-score = 1.4051

x = 74 + ( 1.4051 * 8)

x = 85.2408

rounding to nearest whole number

x2 = 85