A production process produces 90 nondefective parts A sample

A production process produces 90% non-defective parts. A sample of 10 parts from the production process is selected. Assume that this process follows a binomial distribution.

a. What is the probability that the sample will contain exactly 7 non-defective parts?

b. What is the probability that the sample will contain at least 4 defective parts?

c. What is the probability that the sample will contain at least 9 non-defective parts?

d. What is the probability that the sample will contain no defective parts?

e. What is the expected number of defective parts from the sample?

Solution

A production process produces 90% non-defective parts. A sample of 10 parts from the production process is selected. Assume that this process follows a binomial distribution.

n=10

non defective p=0.9

a. What is the probability that the sample will contain exactly 7 non-defective parts?

P(x=7) = 0.0574

b. What is the probability that the sample will contain at least 4 defective parts?

n=10

defective p=1-0.9 =0.1

P( x>=4) = 0.0128

c. What is the probability that the sample will contain at least 9 non-defective parts?

n=10

non defective p=0.9

P( x >=9) =0.7361

d. What is the probability that the sample will contain no defective parts?

n=10

defective p=1-0.9 =0.1

P( x=0) = 0.3487

e. What is the expected number of defective parts from the sample?

n=10

defective p=1-0.9 =0.1

expected number of defective parts from the sample =

Expectation = np = 10*0.1= 1