(1 point) The professor of a introductory calculus class has stated that, histor

Question

(1 point) The professor of a introductory calculus 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 -62% and a standard deviation of -11 %. If using/finding z-values, use three decimals. a) What is the probability that a random chosen final exam mark in this course will be at least 74%? Answer to four decimals. b In order to pass this course, a student must have a final exam mark of at least 50% exam? Use four decimals in your answer. what proportion of students will not pass the calculus final c) The top 5% of students writing the final oxam will receive a letter grade of at least an A in the course. To two decimal places, find the minim um final exam mark needed on the calculus final to earn a letter grade of at least an A in the courso. (d) Suppose this professor randomly picked 26 final exams, observing the earned mark on each. What is the probability that 4 of these have a final exam grade of less than 50%? Use four d0Cimals in your answer

Explanation / Answer

6. Answer to the question is as follows:

a. P(X>=74) = P(Z>= (74-62) / 11) = 0.138

b. P(X>=50) = P(Z>= (50-62)/11)) = 0.862

c. P(X>=c) = P(in top 5%) = P(X>=c) = .05

(c-50)/11 = 1.645

c= 11*1.645+50 = 68.1

So, 68.1%

c.

n = 26

x = 4

p (grade less than 50%) = P(X<50%) = 0.138

Hence,

P(n,x,p)

= P(26,4,.138)

= 26C4(.138^4)(.862)^22

= 0.2067

Answer is 0.2067

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