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how do i find parts A & B to question 2 A company determines that one out of 25

ID: 3170067 • Letter: H

Question

how do i find parts A & B to question 2

A company determines that one out of 25 of the pens it produces is defective. A random sample of 30 pens tested and the number of defective pens is counted. The number of defective pens out of 30 fits a ______ situation. Define the random variable: X =______ Number of trials: n =_____ Success for this situation is______ Probability of success: p =______Probability of failure: q = _____ Write each of the following as a probability, i.e. P(X lessthanorequalto 2), and find the probability: a) Find the probability that none of the pens is defective. b) Find the probability that three of the pens are defective. c) Find the probability that less than two of the pens are defective. d) Find the probability that the number of defective pens is at least ten. e) Find the probability that between three and five of the pens are defective. f) Find the mean and standard deviation for the number of defective pens in a sample of 30 pens.

Explanation / Answer

Binomial

X = No of defective pens

n= 30

Success: a pen is defective

p = 1/25

q = 24/25

A) none of the pens are defective means X=0

P(X=0) = 30C0 x p0 x q30

= (24/25)30

= 0.294

B) P(3 pens are defective)

= P(X=3) = 30C3 x (1/25)3 x (24/25)(30-3)

= 0.086