Question

Suppose that the success rate on a very long statistics test is 75%. For a 10-item quiz(with no partial credit), calculate the probability that a student will get: a. at least 7 items correct b. fewer than 6 items correct(and therefore fail the quiz.) c. 9 or 10 items correct(and get an A on the quiz) d. what is the expected number of items that the student will get correct? e. what is the standard deviation of the number of items that the student will get correct?

Answer 1

this is binomial distribution with parameter n=19 and p=0.75

a)

P( at least 7 items correct )=P(X>=7)==0.7759

b)

fewer than 6 items correct =P(X<=5)= =0.0781

c)

9 or 10 items correct = =0.2440

d) expected number of items that the student will get correct =np=10*0.75 =7.5

e)

standard deviation of the number of items that the student will get correct =sqrt(np(1-p)=sqrt(10*0.75*0.25)=1.3693