Question

Problem #7: Suppose that 26% 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 175 shafts, find the approximate probability that between 37 and 53 (inclusive) are nonconforming and can be reworked. (b) In a random sample of 175 shafts, find the approximate probability that at least 49 are nonconforming and can be reworked.

Answer 1

7)

Answer:

Given that

Suppose that 26% of all steel shafts produced by a certain process are nonconforming but can be reworked

n=175

p=0.26

Normal approximation:

mean=np=175*0.26=45.5

stabdard deviation=sqrt(175*0.26*(1-0.26))=5.8026

a) In a random sample of 175 shafts, find the approximate probability that between 37 and 53 are nonconforming and can be reworked

Use continuity correction factor of 0.5

z(36.5)=(36.5-45.5)/5.8026

= -9/5.8026

  = -1.551

z(53.5) = (53.5-45.5)/5.8026

= 8/5.8026

= 1.378

P(-1.551<z<1.378) = P(z<1.378)-P(z<-1.551)

    = 0.9162- 0.0606

= 0.8556

b) In a random sample of 175 shafts, find the approximate probability that at least 49 are nonconforming and can be reworked.

z=(48.5-45.5)/5.8026

z =3/5.8026

z = 0.5171

P(z>=0.5171) = 0.3015

For the remaining problems please post again friend as per HOMEWORKLIB RULES first question should be the answer when multiple questions are posted. If you have any doubt please ask me friend and if you are satisfied with my solution please give me thumb up.