Question

The professor of a Statistics class has stated that, historically, the distribution of final exam grades in the course resemble a Normal distribution with a mean final exam mark of μ=60μ=60% and a standard deviation of σ=9σ=9%.

(a) What is the probability that a random chosen final exam mark in this course will be at least 73%? Answer to four decimals.

equation editor

(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 calculus final exam? Use four decimals in your answer.

equation editor

(c) The top 4% of students writing the final exam will receive a letter grade of at least an A in the course. To two decimal places, find the minimum final exam mark needed on the calculus final to earn a letter grade of at least an A in the course.

equation editor

%

(d) Suppose this professor randomly picked 26 final exams, observing the earned mark on each. What is the probability that 3 of these have a final exam grade of less than 60%? Use four decimals in your answer.

equation editor

Answer 1

Given mean final exam mark = 60% and standard deviation (SD)= 9%
a) probability that a random chosen final exam mark in this course will be at least 73%

z=(73-60)/9

z=1.44

P(z>=1.44)= 0.0749

b) to pass this course a student must have a final exam mark of at least 50%

z=(50-60)/9

z=-1.11

P(z<-1.11)=0.1335

c) minimum final exam mark needed on the calculus final to earn a letter grade of at least an A in the course.

P(Z>z)=0.04

P(Z<=z)=1-0.04=0.96

z=normsinv(0.96)=1.75

Minimum marks to get A=60+1.75*9=75.75%

d) probability that 3 of these have a final exam grade of less than 60%
z=(60-60)/9

z=0

P ( Z<0 )=0.5

Use binomial distribution with n=26 and p=0.5

P(3 have less than 60%)=26C3*0.5^3*(1-0.5)^23=0.00004