Question

From past record, it is known that a travelling time for a bus from Alor Setar to Kuala Lumpur
are normal distributed with mean 6 hours and standard deviation 1.5 hours. Find probability when
the mean for a random selected of 5 buses are:
i. At most 5 hours
ii. Between 5 and 7 hours
iii. At least 5.5 hours

Answer 1

Given

Let be the sample mean of 5 buses

The sampling distribution of sample mean follow Normal with

mean = 6

and standard error = 1.5/\sqrt{5}=0.6708

that is

then

i)

= P( z < -1.49)

= 0.0681 ( from z table)

Answer : Probability = 0.0681

ii)  

= P(-1.49 < z < 1.49)

= 0.8638 (from z table)

Answer : Probability = 0.8636

iii)  

= P( z >- 0.75 )

= 0.7297 ( from z table)

Answer : Probability = 0.7297