Question

The time of travel from a person's apartment to the bus station follows a uniform distribution over the interval from 20 to 30 minutes. If he/she leaves home at 9:05 AM, what is the probability that he/she will get to the station between 9:20 and 9:25 AM?

0.75

1.0

0

0.25

0.5

Answer 1

Solution-

According to question, the time of travel from a person's apartment to the bus station follows a uniform distribution over the interval from 20 to 30 minutes.

If means a = 20 minutes and b = 30 minutes.

So, Probability density function for this uniform distribution is

f(X) = 1/(b- a) = 1/(30 -20) = 1/10 =0.10

So, Pdf is

f(X) = 0.10 ; X belongs to [20 , 30]

= 0 ; Otherwise

Now, If someone leaves home at 9:05 AM then the probability that he/she will get to the station between 9:20 and 9:25 AM is

= P[ She reaches between 15 minutes (9:05 AM to 9:20 AM )and 20 minutes (9:05 AM to 9:25 AM) ]

= P (15 < X < 20)

= (15-20)×f(X)

= 5×0 = 0

(Because 15 to 20 minutes is not lies in the given internal over which uniform density function is defined).