5. The percentage of accounting undergraduates passing the CPA exam is 20% (assume every student takes...
5. The percentage of accounting undergraduates passing the CPA exam is 20% (assume every student takes the test). You randomly select 17 graduating accounting students and would like to know a few things about their prospects of passing the test. (14 points) a) What distribution would be appropriate for this question? Why? b) What is the probability that exactly 5 will pass the exam? c) What is the probability that at least 9 will pass the exam? d) What is the probability that less than 4 will pass the exam? e) Calculate the mean, variance, and standard deviation of the number of people passing the exam in this sample?
Homework Answers
a)
this is binomial distribution as events are independent and number of trails are fixed
b)
probability that exactly 5 will pass the exam =P(X=5)=17C5(0.2)5(0.8)12 =0.136076
c)
probability that at least 9 will pass the exam =P(X>=9)=0.002581
d)
probability that less than 4 will pass the exam
=P(X<4)=
=0.548876
e)
mean =np=17*0.2=3.4
variance =np(1-p)=2.72
std deviation =sqrt(np(1-p)=sqrt(2.72)=1.6492
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