Name: ____________________________________
AP Statistics
Uniform Distribution Activity
1) The manager of a large department with three floors reports that the time a customer on the second floor
must wait for an elevator has a uniform distribution ranging from 0 to 4 minutes.
a) Find the mean and standard deviation of x, the time a customer on the second floor waits for an
elevator.
b) Find the probability that a randomly selected customer waits less than 1.5 minutes after pushing the
second-floor elevator button.
2) A bus is scheduled to stop at a certain bus stop every half hour on the hour and the half hour. At the end
of the day, buses still stop every 30 minutes, but due to delays that often occur earlier in the day, the bus is
likely to be late. The director of the bus line claims that the length of time a bus is late is uniformly
distributed and the maximum time that a bus is late is 20 minutes.
a) If the director’s claim is true, what is the expected number of minutes a bus will be
late?
b) If the director’s claim is true, what is the probability that the last bus, on any given day, will be more
than 19 minutes late?
3) The manager of a local soft drink bottling company believes that when a new beverage-dispensing
machine is set to dispense 7 ounces, it in fact dispenses an amount x at random anywhere between 6.5 and
7.5 ounces inclusive. Suppose x has a uniform probability distribution.
a) Is the amount dispensed by the machine a discrete or a continuous random variable?
b) Find the mean and standard deviation for the distribution.
c) What is the probability that for a randomly selected bottle the machine will dispense at
least 6.75 ounces?
d) What is the probability that for a randomly selected bottle the machine will dispense more than 7.25
ounces?
e) What is the probability that for a randomly selected bottle the amount the machine dispenses is within
one standard deviation of the mean?
4) Refer to question 3, what is the probability that each of the next six bottles filled by the new machine will
contain more than 7.25 ounces of beverage? Assume that the amount of beverage dispensed in on e bottle is
independent of the amount dispensed in another bottle.
5) The weather on a tropical island in January is fairly constant. Records indicate that the high temperatures
for each day of the month tend to have a uniform distribution with a range of 15 and a maximum high
temperature of 90F. A tourist arrives on the island on a randomly selected day in January.
a) What is the probability that the temperature will be above 80F?
b) What is the probability that the temperature will be between 80F and 85F?
c) What is the expected temperature?