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?

Solution

Step 1 of 4

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 XPoisson (60)

Now X is approximately normal with

mean(=60 and

Standard deviation()=

=7.75