Question

The time (in minutes) until the next bus departs a major bus depot follows a distribution with f(x) =

1

20

where x goes from 25 to 45 minutes.

• Part (h)

  Find the probability that the time is between 30 and 40 minutes. (Enter your answer as a fraction.)
  
  
  Write the answer in a probability statement. (Enter exact numbers as integers, fractions, or decimals.)The probability of a waiting time more than 30 minutes and  less than 40 minutes is ? , given waiting times ~ U (25, 45).

• Part (k)

  Find the 25th percentile. (Enter your answer as a whole number.)
  
  
  In a complete sentence, state what this means. (Enter your answer as a whole number.)

  This means that 25% of the time, the waiting time is less  than ? minutes.

• Part (l)

  Find the probability that the time is more than 40 minutes given (or knowing that) it is at least 30 minutes. (Enter your answer as a fraction.)

Answer 1

h) probability that the time is between 30 and 40 minutes =(40-30)/20=1/2

The probability of a waiting time more than 30 minutes and  less than 40 minutes is 0.5 given waiting times ~ U (25, 45).

k) 25th percentile =25+0.25*(45-25)=25+0.25*20=30

This means that 25% of the time, the waiting time is less  than 30 minutes

l)

probability that the time is more than 40 minutes given it is at least 30 minutes =P(X>40|X>30)=(45-40)/(45-30)=5/15=1/3