Solution Found!
Using a Distribution to Find Probabilities In Exercise,
Chapter 4, Problem 12E(choose chapter or problem)
Problem 12E
Using a Distribution to Find Probabilities In Exercise, find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities.
Defective Parts An auto parts seller finds that 1 in every 100 parts sold is defective. Find the probability that (a) the first defective part is the tenth part sold, (b) the first defective part is the first, second, or third part sold, and (c) none of the first 10 parts sold are defective.
Questions & Answers
QUESTION:
Problem 12E
Using a Distribution to Find Probabilities In Exercise, find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities.
Defective Parts An auto parts seller finds that 1 in every 100 parts sold is defective. Find the probability that (a) the first defective part is the tenth part sold, (b) the first defective part is the first, second, or third part sold, and (c) none of the first 10 parts sold are defective.
ANSWER:
Solution 12E
Step1 of 4:
From the given problem we have an experiment, In that an auto parts seller finds that 1 in every 100 parts sold is defective.
Here our goal is:
a). We need to find the probability of the first defective part is the tenth part sold.
b). We need to find the probability of the first defective part is the first, second, or third part sold.
c). We need to find the probability of none of the first 10 parts sold are defective.
Step2 of 4:
a).
Let,
Let us consider a random variable ‘x’ it presents the number of defective auto parts. And here ‘x’ follows the geometric distribution with parameters ‘p’. The probability mass function of the geometric distribution is:
Where,