Question

Question Help A manufacturer ships toasters in cartons of 1010. In each​ carton, they estimate a 1010​% chance that any one of the toasters will need to be sent back for minor repairs. What is the probability that in a​ carton, there will be exactly 33 toasters that need​ repair?

Answer 1

The probability that there will be repair exactly 3 toaster is 0.0574.

Explanation:

Binomial Distribution:

A discrete random variable X having the set {0,1,2,3......,n} as the spectrum, is said have a binomial distribution with parameter n= number of trials and p=probability of number of success on an individual trial, if the p.m.f (probability mass function) of X given by,

`P(X=x)=C(n,x)p^x(1-p)^(n-x)` x=0,1,2,......,n

=0 elsewhere

where 0<p<1 and n is a positive integer.

Total number of toaster in cartons(n) = 10.

Probability of number of success on an individual trial p= 10% = 0.10

`\therefore P(X=3)= C(10,3)(0.10)^3(1-0.10)^(10-3)`

`=(10!)/(3!(10-3)!)(0.10)^3)(0.90)^7`

=0.0574

The probability that there will be repair exactly 3 toaster is 0.0574.