A) For each probability and percentile problem, draw the picture.

LetX~ Exp(0.2).

1) Sketch a new graph, shade the area corresponding toP(X<7), and find the probability. (Round your answer to four decimal places.)

2) Sketch a new graph, shade the area corresponding toP(4

3) Sketch a new graph, shade the area corresponding toP(X>7), and find the probability. (Round your answer to four decimal places.)

4) Sketch a new graph, shade the area corresponding to the 40th percentile, and find the value. (Round your answer to two decimal places.)

B)According to a study by Dr. John McDougall of his live-in weight loss program at St. Helena Hospital, the people who follow his program lose between 6 and 15 pounds a month until they approach trim body weight. Let's suppose that the weight loss is uniformly distributed. We are interested in the weight loss of a randomly selected individual following the program for one month.

1) Find the probability that the individual lost more than 11 pounds in a month. (Enter an exact number as an integer, fraction, or decimal.)

2) Suppose it is known that the individual lost more than 8 pounds in a month. Find the probability that he lost less than 13 pounds in the month. (Enter an exact number as an integer, fraction, or decimal.)

C)Suppose that the length of long distance phone calls, measured in minutes, is known to have an exponential distribution with the average length of a call equal to10minutes.

1) Find the probability that a phone call lasts less than 12 minutes. (Round your answer to four decimal places.)

2) Find the probability that a phone call lasts more than12minutes. (Round your answer to four decimal places.)

3) Find the probability that a phone call lasts between 8 and 12 minutes. (Round your answer to four decimal places.)

4) If 35 phone calls are made one after another, on average, what would you expect the total to be (in minutes)?

D)The time (in years)afterreaching age 60 that it takes an individual to retire is approximately exponentially distributed with a mean of about7years. Suppose we randomly pick one retired individual. We are interested in the time after age 60 to retirement.

1)Find the probability that the person retired after age71. (Round your answer to four decimal places.)

2)In a room of 1000 people over age78, how many do you expect will NOT have retired yet? (Round your answer to the nearest whole number (of people)).

E) The cost of all maintenance for a car during its first year is approximately exponentially distributed with a mean of$150.

1)Find the probability that a car required over$300for maintenance during its first year. (Round your answer to four decimal places.)

F)

The age of a first grader on September 1 at Garden Elementary School is uniformly distributed from5.6to6.6years. We randomly select one first grader from the class.

1)Find the probability that a first grader is over6years. (Enter your answer as a fraction.)

2)Find the probability that a first grader is between 4 and 6 years. (Enter your answer as a fraction.)

3)Find the70thpercentile for the age of first graders on September 1 at Garden Elementary School. (Enter your answer to one decimal place,in years).