Question

On a certain run of a commuter train, the average number of passengers is 476 and the standard deviation is 22. Assume the variable is normally distributed. If the train makes the run, find the probability that the number of passengers will be a. Between 476 and 500 passengers b. Less than 450 passengers c. More than 510 passengers

Answer 1

Explanation:

Let X be number of passengers will be on a commuter train

Given that X is normal with mean =476 and std deviation=22

Or we can say that

`z=(x-476)/(22) is N(0,1)`

a) Probability that the number of passengers will be Between 476 and 500 passengers

`=P(476<x<500)\\=P(0<x<1.09)\\=0.3621`

b) Probability that the number of passengers Less than 450 passengers

`=P(x<450)\\=P(Z<(-26)/(22) )\\=0.5-0.3810\\=0.1190`

c) Probability that the number of passengers More than 510 passengers

`=P(x>510)\\= P(Z>1.55)\\=0.5-0.4394\\=0.0606`