Probability at least 4 samples contain more than 3 mg....

[tuzzi-i]

The mass of the suspended particles in a sample of water taken from a river can be assumed to be a random variable distributed normally. The mean and standard deviation for the mass of suspended particles are 2.5mg and 1.17mg respectively. Find the probability that out of 5 samples of the river water that is known to contain more than 2 mg suspended particles, at least 4 samples contain more than 3mg suspended particles.

the answer given is 0.3525.

 

[tkhunny]

One Sample

(2-2.5)/1.17 = -0.42735

(3-2.5)/1.17 = 0.42735

Five Samples

(2-2.5)/(1.17/sqrt(5)) = -0.95558

(3-2.5)/(1.17/sqrt(5)) = 0.95558

Now what?