a b will calculate the product ofa and b choose(nx) will calculate ncr ie.. hons

Question

a b will calculate the product ofa and b choose(nx) will calculate ncr ie.. honsets 10 dbinemINA p) will calculate binomial probability at A-, with number of trial probability of success p m(dbinom 2, a will calculate P(x1 sXSAz) with binomial distr with number of trial n and probability of suocess p dpois(x, A) will calculate the Poisson probability at and parameter sum(dpoistxi:s2., 1) will calculate P(xl X S r2) with binomial distributio number of trials n and probability of success p A manufacturer of metal pistons finds that on the average, %10" of his Pistons are rej because they are either oversize or undersize ira balch of20 pistons are considered. w a) no more than 5 rejects? b) at least s rejects? between 5 to 12 rejects linc uding both values? (dl How many rejeets do you expect from the above selected batoh?

Explanation / Answer

Since R code is requested, I am providing the answer in R code with comments:

#Rcode start:

#Clear environment
rm(list=ls())

#The problem follows a binomial distribution, there are only two outcomes, piston rejected with a probability of 10% or p = 0.1 and accepted with a probability of 1- p = 0.9
#Sample size; n = 20
n<-20

#Qn(a) no more than 5 rejects:
#We can get the answer by applying the function dbinom()as below
sum(dbinom(0:5,20,0.1))#Taking probablity of all possible number of rejects till 5 rejects
#Output and Answer:0.9887469, the probability of no more than 5 rejects is 98.8747%
#Qn(b) at least 5 rejects
##We can get the answer by applying the function dbinom()as below
sum(dbinom(5:20,20,0.1))
#Answer: 0.0431745, Hence probability of at least 5 rejects is 4.3175 %
#Qn(C): between 5 to 12 rejects
#Function dbinom
sum(dbinom(5:12,20,0.1))
#Answer: 0.04317449, Probability of 5-12 rejects is 4.3174%
#Qn(d): How many rejects do you expect from the above selected batch
#The question asks about the expection
#the expectation for a binomial distribution is given by, Expectation = np ( 20 *0.1)
20*0.1
#Answer is 2, the expected rejects in 20 pistons is 2

#Rcode end

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