Question

L M NULES ASR FUUF Tedurer The quality-control inspector of a production plant will reject a batch of syringes if two or more defective syringes are found in a random sample of six syringes taken from the batch. Suppose the batch contains 5% defective syringes. (a) Make a histogram showing the probabilities of r-0, 1, 2, 3, ..., 5 and 6 defective syringes in a random sample of six syringes. 0.80 0.80 0.70 0.60 PIT) 0.80 0.80 0.70 0.70 0.60H 0.601 0.50 0.50 0.40 030 0.10 (b) Find M. (Enter your answer to two decimal places.) syringes - What is the expected number of defective syringes the inspector will find? (Enter your answer to two decimal places.) syringes (c) What is the probability that the batch will be accepted? (Round your answer to three decimal places.) (d) Find 0. (Round your answer to three decimal places) syringes

Answer 1

Solution: Given that n = 6, r = 0,1,2,3,4,5,6, p = 0.05
Binomial distribution :P(X=r) = nCr*p^r*q^(n-r)

=> option C.

x P(X)
0 0.7351
1 0.2321
2 0.0305
3 0.0021
4 0.0001
5 0.0000
6 0.0000

(d) μ = 0.30

=> μ = ∑x*p(x)
= (0*0.7351)+(1*0.2321)+(2*0.0305)+(3*0.0021)+(4*0.0001)+(5*0)+(6*0)
= 0.2998
= 0.30 (rounded)

Expected number = n*p = 6*0.05 = 0.3

(c) P(X >= 2) = 0.8906 = 0.891 (rounded)

(d) standard deviation = sqrt(npq) = sqrt(6*0.05*0.95) = 1.225 (rounded)