Question

The time that it takes for the next train to come follows a Uniform distribution with f(x) =1/30 where x goes between 1 and 31 minutes. Round answers to 4 decimal places when possible. a. This is a distribution. b. It is a distribution. c. The mean of this distribution is d. The standard deviation is e. Find the probability that the time will be at most 20 minutes. f. Find the probability that the time will be between 9 and 11 minutes. g. Find the 7th percentile. h. Find the probability that the time is more than 24 minutes given (or knowing that) it is at least 7 minutes.

Answer 1

a)

This is a continuous distribution

b)

It is a uniform distribution

c) mean of this distribution =(31+1)/2=16

d)

The standard deviation is =(31-1)/sqrt(12)=8.6603

e)

e probability that the time will be at most 20 minutes =P(X<20)=(20-1)/(30)=0.6333

f)

probability that the time will be between 9 and 11 minutes =(11-9)/30=0.0667

g) 7th percentile =1+0.07*(31-1)=3.1

h) probability that the time is more than 24 minutes given (or knowing that) it is at least 7 minutes

=P(X>24|X>7)=(31-24)/(31-7)=0.2917