Question

Suppose that 10% of all steel shafts produced by a certain process are nonconforming but can be reworked (rather than having to be scrapped). Consider a random sample of 200 shafts, and let X denote the number among these that are nonconforming and can be reworked.
(a) What is the (approximate) probability that X is at most 30?

(b) What is the (approximate) probability that X is less than 30?

(c) What is the (approximate) probability that X is between 15 and 25 (inclusive)?

Answer 1

Answer:

0.9905,0.9837,0.8066

Step-by-step explanation:

Given that 10%  of all steel shafts produced by a certain process are nonconforming but can be reworked (rather than having to be scrapped).

Each shaft is independent of the other and probability for non conforming is the same for each trial.

Hence X the among these that are nonconforming and can be reworked. is Bin with n =200 and p = 0.10

a) $P(X\leq 30) = 0.9905$

b) $P(X$

c) $P(15\leq x\leq 25)\\= F(25)-F(14)\\= 0.8995-0.0929\\= 0.8066$