Question

Quality control checks a batch of 1000 pairs of glasses and finds 5 with scratches. Assuming this proportion holds for other​ batches, find the probability that no more than 15 pairs of glasses are scratched in a batch of 5000.

The probability is:

(Round to 4 decimal places)

Answer 1

Answer)

N = 5000

P = 5/1000

First we need to check the conditions of normality that is if n*p and n*(1-p) both are greater than 5 or not

N*p = 25

N*(1-p) = 4975

Both the conditions are met so we can use standard normal z table to estimate the probability

P(x<=15)

By continuity correction

P(x<15.5)

Z = (x - mean)/s.d

Mean = n*p = 25

S.d = √{n*p*(1-p)} = 4.98748433581

Z = (15.5 - 25)/4.98748433581 = -1.9

From z table, P(z<-1.9) = 0.0287