Question

Number of passengers who arrive at the platform in an amtrack train station for the 2 pm train on a saturday is a random variable with a mean of 180 and a standard deviation of 25.
a.with what probability can we assert that there will be between 80 and 280 passengers?
b.with what probability can we assert that there will be between 130 and 230 passengers?

Answer 1

Assuming a normal distribution  we find the standardized z scores for  a:-

z1 = (80 - 180)  / 25  =  = -100/25  = -4
z2 =  (280-180) / 25  =  4
Required P( -4 < z < 4)  from the tables is  >99.9%

b
z1 = 130-180 / 25 =  -2
z2 =  230-180 / 25  = 2

from tables probability is 2* 0.4773  =  95.46 %