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# The concentration of particles in a suspension is 30 per ISBN: 9780073401331 38

## Solution for problem 14E Chapter 4.11

Statistics for Engineers and Scientists | 4th Edition

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Problem 14E

Problem 14E

The concentration of particles in a suspension is 30 per ml.

a. What is the probability that a 2 ml sample will contain more than 50 particles?

b. Ten 2 ml samples are drawn. What is the probability that at least 9 of them contain more than 50 particles?

c. One hundred 2 ml samples are drawn. What is the probability that at least 90 of them contain more than 50 particles?

Step-by-Step Solution:

Step 1 of 4</p>

Let X is the no.of particles in the sample

For one ml the concentration of particles in a suspension is 30

a) Here we have to find the probability that a 2 ml sample will contain more than 50 particles

For 2 ml the concentration of particles in a suspension is 2(30)= 60

Here X Poisson (60)

Now X is approximately normal with

mean( =60 and

Standard deviation( )= =7.75

Step 2 of 4</p>

Now P(X>50)

Using the continuity correction find Z value for 50.5

Z=( Z=(50.5 - 60)/7.75

=-1.23

Now find P(Z>-1.23)=1-P(z -1.23)

=1-0.10935

=0.89065

The probability that a 2 ml sample will contain more than 50 particles is 0.89065

Step 3 of 4

Step 4 of 4

##### ISBN: 9780073401331

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The concentration of particles in a suspension is 30 per

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