Chapter 5, Problem 82H

The time (In minutes) until the next bus departs a major bus depot follows a distribution with $f\left(x\right)=\frac{1}{20}$ where x goes

from 25 to 45 minutes.

a. Define the random variable. X = ________

b. X $\sim$________ .

c. Graph the probability distribution.

d. The distribution Is ______________ (name of distribution). ft Is _____________ (discrete or continuous).

e. $\mu$ =______ .

f. $\sigma$ = ______

g. Find the probability that the time is at most 30 minutes. Sketch and label a graph of the distribution. Shade the area of interest. Write the answer in a probability statement.

h. Find the probability that the time is between 30 and .10 minutes. Sketch and Label a graph of the distribution. Shade the area of interest. Write the answer in a probability statement.

i. P(25 < x 55) = _________. State this in a probability statement, similarly to parts g and h, draw the picture, and find the probability.

j. Find the 90th percentile. This means that 90% of the time, the time is less than _ ___ minutes.

k. Find the 75th percentile. In a complete sentence, state what this means. (See pan J.)

j. Find the probability that the time Is more than .10 minutes given (or knowing that) it is at least 30 minutes.