Question

In: Statistics and Probability

A lot of 100 washers contains 5 in which the variability in thickness around the circumference...

A lot of 100 washers contains 5 in which the variability in thickness around the circumference of the washer is unacceptable. A sample of 10 washers is selected at random, without replacement. (Round your answer to four decimal places.)


(a) What is the probability that none of the unacceptable washers is in the sample?

(b) What is the probability that at least one unacceptable washer is in the sample?

(c) What is the mean number of unacceptable washers in the sample?

Solutions

Expert Solution

A lot of 100 washers contains 5 in which the variability in thickness around the circumference of the washer is unacceptable.

Therefore,

p: When a washer is selected at random from the lot of 100, Probability of selecting an unacceptable washer =5/100 =0.05

n : number of washers selected = 10

X : Number of unacceptable washers in the sample

X follows a Binomial distribution with n=10 and p=0.05

Probability mass function of X is given by

Probability of 'r' unacceptable washers in the sample

(a) What is the probability that none of the unacceptable washers is in the sample?

probability that none of the unacceptable washers is in the sample = P(X=0)

Probability that none of the unacceptable washers is in the sample = 0.5987

(b) What is the probability that at least one unacceptable washer is in the sample?

Probability that at least one unacceptable washer is in the sample = P(X1)

P(X1) = 1-P(X=0) =1-0.5987=0.4013

Probability that at least one unacceptable washer is in the sample = 0.4013

(c) What is the mean number of unacceptable washers in the sample?

Mean (Expected value ) of binomial distribution = np

Mean number of unacceptable washers in the sample = 10 x 0.05 =0.5

mean number of unacceptable washers in the sample = 0.5

orchestra answered 2 years ago
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