sample size?

Question

A large hospital wants to estimate the mean time before the patients are attended upon arrival to the hospital emergency room. From a past study it is known that the standard deviation of the waiting room time is 12 minutes. If the hospital administration wishes to estimate the mean time within 3 minutes with a 95% confidence, the sample size needed will be?

(I've tried this a few times don't know if i'm doing the problem right. i tried twice and i got two different answers. 1st time if got 190 then the second time i got 290.)

thanks for helping me.

Answer 1

max error = zσ/n = 3  

 

you know st.dev.=12 and z=1.96; substitute and solve for n