Question

Ceramics in a factory are manufactured in lots of 200 and 3% are defective. Assume the pieces are independent. Use the normal approximation to the binomial with the continuity correction to find the probability more than 10 are defective.
0.031 (Correct)
And, use the normal approximation to the binomial with the continuity correction to find the probability there are between 4 and 8 defects, inclusive.
0.5832 (incorrect)

I try the second question but my answer is in correct.

Answer 1

n=	200	p=	0.0300
here mean of distribution=μ=np=		6
and standard deviation σ=sqrt(np(1-p))=		2.4125
for normal distribution z score =(X-μ)/σx
therefore from normal approximation of binomial distribution and continuity correction:

a)

  probability more than 10 are defective:

probability =

P(X>10.5)

=

P(Z>1.865)=

1-P(Z<1.87)=

1-0.9689=

0.031

b)

probability there are between 4 and 8 defects:

probability =

P(3.5<X<8.5)

=

P(-1.04<Z<1.04)=

0.85-0.15=

0.6999

( please try 0.7016 if above comes incorrect due to rounding error)