Question

Using R to solve the problem, please copy and paste your code. Thanks. (You must use R)

8. (15 pts) Consider the following questions: give the distribution name, carefully define the random variables you use and find the final answer.

(a) (3 pts) A professor has made 20 exams of which 8 are hard, 7 are reasonable, and 5 are easy. The exams are mixed up and the professor selects 4 of them at random to give to four sections of the course she is teaching. What is the probability that no sections receive a hard test?

(b) (3 pts) Suppose a representative at a credit card customer service center receives a phone call every 5 minutes on average. Find the probability that she receives 3 phone calls in 20 minutes.

(c) (3 pts) Products produced by a machine has a 3% defective rate. What is the probability that the first defective occurs in the fifth item inspected.

     

(d) (3 pts) In a class of 100 students, 25 have hardcover and 75 students have paperback textbooks. If you randomly choose 10 students in this class, find the probability that 2 of them have hardcover texts.

Answer 1

rm(list=ls(all=TRUE))
> #problem a
> #this is a binomial distribution with r.v number of section receied hard test
> p1=dbinom(0,4,0.4);p1#p=4/20,n=4,x=0
[1] 0.1296
>
>
> #problem b
> #this is problem of poisson distribtion with parameter lambda=(1/5)*20
> #here random variable is no. of phone calls received
> p2=dpois(3,4);p2
[1] 0.1953668
>
> #problem c
> #this is a problem of geometric distribution with p=0.03 and q=0.97 and x=4
> #here the random variable is non defective before first defective
> p3=dgeom(4,0.03);p3
[1] 0.02655878
>
> #problem d
> #here we will use binomial distribution with n=10,p=0.25
> #r.v is no. of hard cover text
> p4=dbinom(2,10,0.25);p4
[1] 0.2815676
>