Question

Problem #7: Suppose that 30% 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 238 shafts, find the approximate probability that between 61 and 82 (inclusive) are nonconforming and can be reworked. (b) In a random sample of 238 shafts, find the approximate probability that at least 73 are nonconforming and can be reworked. Problem #7(a): Round your answer to 4 decimals. Problem #7(b): Round your answer to 4 decimals. Just Save Submit Problem #7 for Grading Attempt #5 7(a) Problem #7 Attempt #1 | Attempt #2 | Attempt #3 | Attempt #4 Your Answer: 7(a) 7(a) 7(a) 7(a) 7(b) 7(b) 7(b) Your Mark: 7(a) 7(a) 7(a) 7(b) 716) Attempt #7 7(a) 7(b) Attempt #6 7(a) 7(b) 7(a) | 7(b) 7(6) Attempt #9 7a) 7(b) 7(b) Attempt #8 7(a) 7(6) 7(a) 7(b) 7(a) 7(a) 7(b) 7(a) 7(b) 7(b) 7(b)

Answer 1

n=	238	p=	0.3000
here mean of distribution=μ=np=		71.4
and standard deviation σ=sqrt(np(1-p))=		7.0697
for normal distribution z score =(X-μ)/σx
therefore from normal approximation of binomial distribution and continuity correction:

a)

probability =

P(60.5<X<82.5)

=

P(-1.54<Z<1.57)=

0.9418-0.0618=

0.8800

( please try 0.8802 if this comes wrong)

b)

probability =

P(X>72.5)

=

P(Z>0.16)=

1-P(Z<0.16)=

1-0.5636=

0.4364

( please try 0.4382 if this comes wrong)