The professor of an introductory calculus class has stated that, historically, the distribution of final exam grades in the course resembles a normal distribution with a mean final exam mark of = 63% and a standard deviation of σ = 9%. (a) What is the probability that a randomly chosen final exam mark in this course will be at least 71%? Answer to four decimals. (b) In order to pass this course, a student must have a final exam mark of at least 50%. What proportion of students will not pass the final exam? Use four decimals in your answer. (c) The top 3% of students writing the final exam will receive a letter grade of at least A in the course. To two decimal places, find the minimum final exam mark needed to earn a letter grade of at least A in the course. % (d) Suppose this professor randomly picked 30 final exams, observing the earned mark on each. What is the probability that 3 of these exams will have a grade of less than 50%? Use four decimals in your answer.
The professor of an introductory calculus class has stated that, historically, the distribution of final exam grades in the course resembles a normal distribution with a mean final exam mark of = 63% and a standard deviation of σ = 9%. (a) What is the probability that a randomly chosen final exam mark in this course will be at least 71%? Answer to four decimals. (b) In order to pass this course, a student must have a final exam mark of at least 50%. What proportion of students will not pass the final exam? Use four decimals in your answer. (c) The top 3% of students writing the final exam will receive a letter grade of at least A in the course. To two decimal places, find the minimum final exam mark needed to earn a letter grade of at least A in the course. % (d) Suppose this professor randomly picked 30 final exams, observing the earned mark on each. What is the probability that 3 of these exams will have a grade of less than 50%? Use four decimals in your answer.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter11: Simulation Models
Section: Chapter Questions
Problem 54P
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![The professor of an introductory calculus class has stated that, historically, the distribution of final
exam grades in the course resembles a normal distribution with a mean final exam mark of = 63%
and a standard deviation of σ = 9%.
(a) What is the probability that a randomly chosen final exam mark in this course will be at least
71%? Answer to four decimals.
(b) In order to pass this course, a student must have a final exam mark of at least 50%. What
proportion of students will not pass the final exam? Use four decimals in your answer.
(c) The top 3% of students writing the final exam will receive a letter grade of at least A in the
course. To two decimal places, find the minimum final exam mark needed to earn a letter grade of at
least A in the course.
%
(d) Suppose this professor randomly picked 30 final exams, observing the earned mark on each.
What is the probability that 3 of these exams will have a grade of less than 50%? Use four decimals
in your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F037bb951-2009-4779-b99f-ef4772de4899%2Fdccd6368-b431-43d8-aeba-8ab58e1db41e%2Fqucz0aa_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The professor of an introductory calculus class has stated that, historically, the distribution of final
exam grades in the course resembles a normal distribution with a mean final exam mark of = 63%
and a standard deviation of σ = 9%.
(a) What is the probability that a randomly chosen final exam mark in this course will be at least
71%? Answer to four decimals.
(b) In order to pass this course, a student must have a final exam mark of at least 50%. What
proportion of students will not pass the final exam? Use four decimals in your answer.
(c) The top 3% of students writing the final exam will receive a letter grade of at least A in the
course. To two decimal places, find the minimum final exam mark needed to earn a letter grade of at
least A in the course.
%
(d) Suppose this professor randomly picked 30 final exams, observing the earned mark on each.
What is the probability that 3 of these exams will have a grade of less than 50%? Use four decimals
in your answer.
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