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1. A college professor teaches Chemistry 101 each fall to a large class of first-year students. For tests, she uses standardized exams that she knows from past experience produce normal distributions of scores, with a mean of 70 and a standard deviation of 12. a. Her philosophy of grading is to impose standards that will yield, in the long run, 14% A's, 20% B's, 32% C's, 20% D's and 14% F's. Where should the cutoff be between the A's and the B's? Between the B's and the C's? b. According to reference tables, will a standard normal distribution have any points above 2.5? How does that translate to the distribution of scores? c. What share of points in a standard normal distribution are below -4? What does that imply for the distribution of scores?

1. A college professor teaches Chemistry 101 each fall to a large class of first-year students. For tests, she uses standardized exams that she knows from past experience produce normal distributions of scores, with a mean of 70 and a standard deviation of 12. a. Her philosophy of grading is to impose standards that will yield, in the long run, 14% A's, 20% B's, 32% C's, 20% D's and 14% F's. Where should the cutoff be between the A's and the B's? Between the B's and the C's? b. According to reference tables, will a standard normal distribution have any points above 2.5? How does that translate to the distribution of scores? c. What share of points in a standard normal distribution are below -4? What does that imply for the distribution of scores?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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1. A college professor teaches Chemistry 101 each fall to a large class of first-year students. For tests, she uses standardized exams that she knows from past experience produce normal distributions of scores, with a mean of 70 and a standard deviation of 12. a. Her philosophy of grading is to impose standards that will yield, in the long run, 14% A's, 20% B's, 32% C's, 20% D's and 14% F's. Where should the cutoff be between the A's and the B's? Between the B's and the C's? b. According to reference tables, will a standard normal distribution have any points above 2.5? How does that translate to the distribution of scores? c. What share of points in a standard normal distribution are below-4? What does that imply for the distribution of scores?
Transcribed Image Text:1. A college professor teaches Chemistry 101 each fall to a large class of first-year students. For tests, she uses standardized exams that she knows from past experience produce normal distributions of scores, with a mean of 70 and a standard deviation of 12. a. Her philosophy of grading is to impose standards that will yield, in the long run, 14% A's, 20% B's, 32% C's, 20% D's and 14% F's. Where should the cutoff be between the A's and the B's? Between the B's and the C's? b. According to reference tables, will a standard normal distribution have any points above 2.5? How does that translate to the distribution of scores? c. What share of points in a standard normal distribution are below-4? What does that imply for the distribution of scores?
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