A machine contains 10 processors that operate independently. The proba

arneguet9k

arneguet9k

Answered question

2021-11-16

A machine contains 10 processors that operate independently. The probability that a processor fails is 0.08
(a) What is the probability that exactly 4 of the processors fail?
(b) What is the probability that at most 1 of the processors fails

Answer & Explanation

Bromodermgs

Bromodermgs

Beginner2021-11-17Added 8 answers

Step 1: Given information
A machine contains 10 processors that operate independently.
The probability that a processor fails is 0.08
Here,
Sample size, n=10
Probability, p=0.08
Step 2: Probability is given by,
By using Binomial distribution, we have
a) The probability that exactly 4 of the processors fail is given by,
P(X=4)=(104)(0.08)4(10.08)104P(X=4)=0.0052
(Round to four decimal places)
By using EXCEL-BINOMDIST(4,10,0.08,0)
b) The probability that at most 1 of the processors fails is given by,
P(X1)=0.8121
By using EXCEL-BINOMDIST(1,10,0.08,1)
(Round to four decimal places)

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