Question

Central Limit Theorem

The arrival of Blue Loop buses to the Penn State library stop can be modeled as a Poisson process. Buses are scheduled to arrive every 15 minutes. You and your friends are making observations at the library stop during different times of the day. You and your friends observe 53 Blue Loops arrivals, and you record the inter-arrival times (i.e. the time between the arrival of the n^th and the (n+1)^st bus in minutes.

1. What is the probability that the average arrival time that you and your friends observe for the Blue Loop is less than 15.7 minutes? (Use 3 decimal places)

Answer 1

here for poisson distribution mean =15 and std deviation of one observation =sqrt(15.0)=3.873

for normal distribution z score =(X-μ)/σx
here mean=       μ=	15
std deviation   =σ=	3.8730
sample size       =n=	53
std error=σx̅=σ/√n=	0.5320

probability that the average arrival time that you and your friends observe for the Blue Loop is less than 15.7 minutes :

probability =

P(X<15.7)

=

P(Z<1.32)=

0.907

( please try 0.906 if this comes wrong and revert)