Question

Suppose that 24% of all steel shafts produced by a certain process are nonconforming but can be reworked (rather than having to be scrapped).

(a)	In a random sample of 183 shafts, find the approximate probability that between 29 and 52 (inclusive) are nonconforming and can be reworked.

(b)	In a random sample of 183 shafts, find the approximate probability that at least 48 are nonconforming and can be reworked.

Answer 1

Ans. p=24% = 0.24, n=183

This is binomial probability, the pmf is

Where, n = total number of trials

p = probability of successes in single trial

x = number of successes

Note :- We find answers using R:-

> #(a). P(29<=X<=52)
> sum(dbinom(x=29:52,183,prob=0.24))
[1] 0.9264032
> # P(29<=X<=52) = 0.9264
>
> #(b). P(X>=48)
> sum(dbinom(x=48:183,183,prob=0.24))
[1] 0.2647544
> # P(X>=48)=0.2648