A teacher gives a test to a large group of students. The results are closely approximated by a normal curve. The mean is 74, wi

Question

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A teacher gives a test to a large group of students. The results are closely approximated by a normal curve. The mean is 74, wi

th a standard deviation of 8. The teacher wishes to give A's to the top 8% of the students and F's to the bottom 8%. A grade of B is given to the next 16%, with D's given similarly. All other students get C's. Find the bottom cutoff for a grade of C.

Mathematics

1 answer:

Alinara [238K] · Answer 1 · 2023-07-06T13:07:33+03:00

Answer:

Step-by-step explanation:

Given that a teacher gives a test to a large group of students. The results are closely approximated by a normal curve

mu =74 and sigma =8

A grade starts from 100-8 = 92nd percentile

Z score for 92nd percentile = 1.405

X score = 74+8(1.405) = 85.24

--------------------

B cut off is to next 16%

Hence C would start for scores below 100-(8+16) = 76%

76th percentile = 0.705*8+74 =79.64

A teacher gives a test to a large group of students. The results are closely approximated by a normal curve. The mean is 74​, wi

A teacher gives a test to a large group of students. The results are closely approximated by a normal curve. The mean is 74, wi