Question

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

One hundred 2 mL samples are drawn. What is the probability that at least 90 of them contain more than 48 particles?

Answer 1

The random variable X is defined as the number of particles in a 2 m L sample. Then X follows Poisson with a parameter, = 2*30 = 60 mL

Since > 10, by normal approximation X will follow normal distribution with mean and variance .

So,

Now, the probability that a single 2 mL sample contain more than 48 particles is given by, P(X>48)

                          

                          

                          

                          

we use the standard normal table to find area below 1.55

Now, let the random variable Y is defined as the number of samples out of 100 samples that contain more than 48 particles.

Then the random variable Y follows binomial with parameters n=100 and p = 0.9394.

The probability that at least 90 of them contain more than 48 particles, P( Y90).

                   

Answer: 0.96