Question

Assume that 15% of circuit boards used in manufacturing compact displayers are defective. Off a batch of 200 randomly selected such circuit boards, use the normal approximation with the continuity correction to find the probability that at most 30 of these boards are defective. Is your answer approximate or exact.

b. find exact probability using R code to compare answer on the previous question?

Answer 1

a)

p = 0.15

n = 200

We have to find P(X 30)

Using continuity correction factor.

P(X 30) = P(X < 30.5)

Mean = = n*p = 200*0.15 = 30

Standard deviation = = =

For finding above probability we have to find z score.

That is we have to find P(Z < 0.10)

P(Z < 0.10) = 0.5394

( Using z table)

Our answer is approximate.

b)

By using R code we have to find exact probability.

R codes and output

pbinom(30,size = 200,prob = 0.15)
0.5485115

Exact probability = 0.5485115

Both answer near about same!

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