Question

# The time (in minutes) until the next bus departs a major bus depot follows a distribution...

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 1: Find the probability that the time is at most 35 minutes. (Enter your answer as a fraction.)Sketch and label a graph of the distribution. Shade the area of interest. Write the answer in a probability statement. (Enter exact numbers as integers, fractions, or decimals.)

The probability of a waiting time of 35 minutes or is given waiting times ~ ( , )

Part 2:Find the probability that the time is between 35 and 40 minutes. (Enter your answer as a fraction.)Sketch and label a graph of the distribution. Shade the area of interest.Write the answer in a probability statement. (Enter exact numbers as integers, fractions, or decimals.)

The probability of a waiting time( less or more than) ? 35 minutes and ( less or more than)? 40 minutes is  , given waiting times ~  ? U or Exp ( , ).

Part 3:Find P(25 < x < 55). (Enter an exact number as an integer, fraction, or decimal.)

P(25 < x < 55) =

State this in a probability statement. (Enter exact numbers as integers, fractions, or decimals.)

The probability of a waiting time between 25 and 55 minutes is .......  given waiting times ~? ( , ).

Part 4: Find the 90th percentile. (Enter your answer as a whole number.) State what this means in a complete sentence. (Enter your answer as a whole number.)

This means that 90% of the time, the waiting time is (less or more)? Than what? minutes.

Part 5: 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 or more)? Than what? minutes.

Part 6: Find the probability that the time is more than 40 minutes given (or knowing that) it is at least 35 minutes. (Enter your answer as a fraction.)

solution : (1)he probabilty of waiting time is

(2)given waiting times, U is distributed between (35,40)

(3) probabilty of waiting time is

Given waiting times, U is distributed between (25,45).

(4)

The quatile function of X is

(5)The 90th percentile is

(6)

The 25th percentile is

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