In: Statistics and Probability
Suppose the mean wait time for a bus is 30 minutes and the standard deviation is 10 minutes. Take a sample of size n = 100.
Find the 95th percentile for the sample mean wait time.
solution:
Given that,
mean =
= 30
standard deviation =
= 10
n = 100
= 30
=
/
n = 10/
100=1
Using standard normal table,
P(Z < z) = 95%
= P(Z < z) = 0.95
z = 1.65 Using standard normal table,
Using z-score formula
= z *
+
= 1.65*1+30
= 31.65