Question

The population mean is known to be μ =160 and standard deviation σ = 30.

What is the probability of selecting one individual from this population that has a value higher than 190?

Answer 1

We have to calculate the probability that one individual is selected from a population with mean=160 and standard deviation(S.D)=30 is greater than 190

say the individual is X

P[X>190]

=P[(X-160)/30>(190-160)/30]

Now, By Central Limit theorem,

(X_n-mean)/S.D goes to standard normal i.e Normal(mean=0;variance=1)

Here Xn consists of only one observation

Z=(X-160)/30 where Z~N(0,1)

now,  

P[X>190]

=P[(X-160)/30>(190-160)/30]

=P[Z>1] = .1587