Question

Suppose that the probability of a convicted shoplifter repeating the crime within 5 years is .30. Of 200 convicted shoplifters, what is the probability that at least 70 will shoplift again during the next five-year period?

Use the normal approximation to the binomial here. Answer

Answer 1

Solution:

Given that,

P = 0.30

1 - P = 0.70

n = 200

Here, BIN ( n , P ) that is , BIN (200 , 0.30)

then,

n*p = 60 > 5

n(1- P) = 140 > 5

According to normal approximation binomial,

X Normal

Mean = = n*P = 60

Standard deviation = =n*p*(1-p) = 42

We using continuity correction factor

P(X a ) = P(X > a - 0.5)

P(x > 69.5) = 1 - P(x < 69.5)

= 1 - P((x - ) / < (69.5 - 60) / 42 )

= 1 - P(z < 1.47)

= 1 - 0.9292

= 0.0708

Probability = 0.0708