Probability of Samples Containing Less than 1.6 mg of Suspended Particles?

[thereddevils]

Homework Statement

The masses of suspended particles in a sample of water taken from a lake can be assumed to be a random variable which is normally distributed with mean 2.17 and variance 0.979. Find the probability that out of 4 samples of lake water known to contain less than 1.8 mg of suspended particles , at least 3 samples contain less than 1.6 mg of suspended particles.

Homework Equations

The Attempt at a Solution

probability of a sample less than 1.6 mg, P(X<1.6)=0.28227

X-B(4, 0.28227)

P(X>=3)=P(X=3)+P(X=4)=0.071

Probability of all 4 samples contain less than 1.8 mg of suspended particles = (0.3542)^4
= 0.015

So the required probability = 0.071/0.015 = 4.7

obviously that's wrong. Would appreciate if someone can point me to my errors.

 

[vela]

For one, you're using the variable X to represent two different random variables.

You basically have the right idea, but you want to take into account the fact that the samples are known to have less than 1.8 mg of suspended particles right from the start. Instead of using p=P(X<1.6) for the binomial distribution, use p=P(X<1.6|X<1.8).

 

[thereddevils]

For one, you're using the variable X to represent two different random variables.

You basically have the right idea, but you want to take into account the fact that the samples are known to have less than 1.8 mg of suspended particles right from the start. Instead of using p=P(X<1.6) for the binomial distribution, use p=P(X<1.6|X<1.8).

thanks Vela.