Question

When circuit boards used in the manufacture of compact disc players are tested, the long run percentage of defectives is 5%. suppose that a batch of 250 boards has been received and that the condition of any particular board is independent of that of any other board.

a) Calculate the exact probability that at least 10 of the boards in the batch are defective

b) Calculate the approx probability that at least 10 of the boards in the batch are defective using a normal distribution

(Please do these problems using a R software) this is a computer assignment (show work)

Answer 1

Pr(X≥10)=1 - Pr(X≤10)

=1-(Pr(X=0)+Pr(X=1)+Pr(X=2)+Pr(X=3)+Pr(X=4)+Pr(X=5)+Pr(X=6)+Pr(X=7)+Pr(X=8)+Pr(X=9)+Pr(X=10))

Using R

1-pbinom(10, size=250, prob=0.05)

= 1-0.2909254

=0.7090746

Using R

> 1 - pnorm(9.5, mean=12.5, sd=3.445)
[1] 0.8080758