Question

Based on past experience, 7% of all luncheon vouchers are in error. If a random sample of 400 vouchers is selected, what is the approximate probability that (1) exactly 25 are in error? (2) fewer than 25 are in error? (3) between 20 and 25 (inclusive) are in error?

Answer 1

Answer:

P(X =25) = 0.0687

Probability of having fewer error than 25 =  0.2511

Probability between 20 and 25 = 0.2776

Explanation:

Given Data:

probability of success =0.07

number of vouchers 400

1) probability of exactly 25 are in error $P(X =25) =^{400}C_ {25} \times 0.07^{25} \times 0.93^375$

              = 0.0687

B) Probability of having fewer error than 25

P(X<25) = 0.2511

C) Probability between 20 and 25

 =  p(x<25) - p(x<19)

 = 0.3198 - 0.0422 = 0.2776