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Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 4.3 - Problem 5e
Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 4.3 - Problem 5e

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# A data center contains 1000 computer servers. Each server ISBN: 9780073401331 38

## Solution for problem 5E Chapter 4.3

Statistics for Engineers and Scientists | 4th Edition

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Problem 5E

Problem 5E

A data center contains 1000 computer servers. Each server has probability 0.003 of failing on a given day.

a. What is the probability that exactly two servers fail?

b. What is the probability that fewer than 998 servers function?

c. What is the mean number of servers that fail?

d. What is the standard deviation of the number of servers that fail?

Step-by-Step Solution:

Solution

Step 1 of 5

Here the data centre contains 1000 computer servers

So n=1000

The probability of failing each server is 0.003

So, p=0.003

Let X is no.of servers fail

Here X B(1000,0.003)

Since ‘n’ is large and ‘p’ is small

The Binomial distribution will be converted to poisson distribution

The pmf of poisson distribution is P(X)= , X=0,1,2,..............

So, =np

=1000(0.003)

=3

Hence X Poisson (3)

Step 2 of 5

Step 3 of 5

##### ISBN: 9780073401331

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