Question

The length of time it takes to get through the security checks at a very large urban airport is a random variable with mean μ = 20.6 minutes and standard deviation σ = 8.4 minutes. a simple random sample of 36 airline passengers is to be observed going through security. for the passengers in the srs, what is the approximate probability that the mean length of time for them to get through security will be less than 18 minutes?

Answer 1

a) The population and sample mean are always the same ... in this case, it is 20.6 minutes. 

b) First convert the data to z-values: 

P(X<18) = P(z < (18-20.6)/8.4) = P(z< -0.3095) 

Now, using a Standard Normal table, look up z= -0.3095 

P(X<18) = 0.3785 

Hope that helps