Solution Found!
In a certain process, the probability of producing an
Chapter 4, Problem 11SE(choose chapter or problem)
In a certain process, the probability of producing a defective component is 0.07.
a. In a sample of 250 randomly chosen components, what is the probability that fewer than 20 of them are defective?
b. In a sample of 10 randomly chosen components, what is the probability that one or more of them is defective?
c. To what value must the probability of a defective component be reduced so that only 1% of lots of 250 components contain 20 or more that are defective?
Questions & Answers
QUESTION:
In a certain process, the probability of producing a defective component is 0.07.
a. In a sample of 250 randomly chosen components, what is the probability that fewer than 20 of them are defective?
b. In a sample of 10 randomly chosen components, what is the probability that one or more of them is defective?
c. To what value must the probability of a defective component be reduced so that only 1% of lots of 250 components contain 20 or more that are defective?
ANSWER:
Answer:
Step1 of 6:
Given, the probability of producing a defective component is 0.07.
a). The aim is to find the probability that fewer than 20 of them are defective.
Let X be the number of components in a sample of 250 that are defective.
Then,
Where, n = 250, p = 0.07.
Now, compute mean
= (250)(0.07)
= 17.5
And standard deviation (where, q = 1- p = 1- 0.07 = 0.93)
=
= 4.0342