Answer to Question #169647 in Statistics and Probability for Harshdeep Singh

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Item 8Exercise 5-58

A manufacturer of computer chips claims that the probability of a defective chip is 0.005. The manufacturer sells chips in batches of 700 to major computer companies.

 

a. How many defective chips would you expect in a batch? (Round the final answer to 2 decimal places.)

 

Number of chips            

 

b. What is the probability that none of the chips are defective in a batch? (Round the final answer to 4 decimal places.)

 

Probability            

 

c. What is the probability at least one chip is defective in a batch? (Round the final answer to 4 decimal places.)

 

Probability            

Answer 1

We have that

p(defective) = 0.005

n = 700

a. Number of chips = n * p = 0.005 * 700 = 3.50

b. P(none of the chips are defective in a batch) = P(X=0)

this follows binomial distribution and can be calculated by the formula:

$P(X=m)=C(n,m)\cdot p^m \cdot (1-p)^{n-m}$

$P(X=0)=C(700,0)\cdot 0.005^0 \cdot (1-0.005)^{700-0}=0.995^{700}=0.0299$

c. P(at least one chip is defective in a batch) = 1 – P(none of the chips are defective in a batch) = 1 – P(X=0) = 1 – 0.0299 = 0.9701

Answer:

a. 3.50

b. 0.0299

c. 0.9701