In: Statistics and Probability
A total of 350 households were survey in an O-D survey. The average trip length 15 minutes, with a standard deviation of 7 minutes. If 30 households were chosen at random, what is the probability they have an average trip length greater than 12 minutes and less than 30 minutes?
Solution :
Given that ,
mean = = 15
standard deviation = = 7
n = 30
= 15
= / n= 7 / 30=1.2780
P(12< <30 ) = P[(12 -15) / 1.2780 < ( - ) / < (30 -15) /1.2780 )]
= P(-2.35 < Z <11.74 )
= P(Z < 11.74) - P(Z < -2.35)
Using z table
=1 -0.0094
=0.9906
probability= 0.9906