# probability and statistics 33

1. The time to failure of a digital camera (in hours)is distributed exponentially with parameter 10^-4

a) Find the probability that a camera will last less than 9,000 hours or more than 12,000 hours.

b) Find the probability that a camera will last more than 10,000 hours.

c) If a camera has lasted 10,000 hours, find the probability that it will last another 10,000 hours or longer.

2. The pressure of a pressure washer is normally distributed with a mean of 2510 psi and a standard deviation of 90 psi.

a) Find the probability that a randomly selected washer produces pressure below 2400 psi.

b) If all washers with pressure less than 2400 psi or greater than 2600 psi are considered defective find the probability that a randomly selected washer is defective.

c) Determine the value of x so that 99% of all washers have pressure within 2510+/- psi.

3. The number of surface flaws in plastic roll used in the interior of cars has a Poisson distribution with a mean of 0.07 flaws per square foot of plastic roll. Assume a car interior contains 9 square feet of plastic roll

a) What is the probability that there are no surface flaws in a car’s interior?

b) If 10 cars are sold to a rental company, what is the probability that at most one car has surface flaws?

c) If 10 cars are sold to a rental company, what is the expected number of cars with surface flaws?

4. An airline sells 338 tickets for an Airbus A 330-300 flight to Hong Kong which has the capacity of 335 seats.It is

estimated that in the past 97% of all ticketed passengers showed up for the fight

a) Find the probability that the flight will accommodate all ticketed passengers who show up?

b) Find the probability that the fight will depart with empty seats? (10 points)

c)If you are the third person on the standby list (i.c., you will be the third person to get on the plane if there are

available seats), find the probability that you will be able to take the flight? (5 points)