Download worksheet 2 - RIT

SMAM 314
Worksheet 2
Name______________
1. Consider the discrete probability mass function
x 1 2 3 4
f(x) .1 .2 .3 .4
Find
A. P[2 ≤ X ≤ 4]
B. P[X = 1.5]
C. The mean and the variance of X.
D. The cumulative distribution function of X
2. The phone lines to an airline reservation system are occupied 45% of
the time. Assume the events that the lines are occupied on successive calls
are independent. Suppose seven calls are placed to the airline.
A. What is the probability the lines are occupied for exactly four calls?
B. What is the probability the lines are occupied for at most two calls?
3. Messages arrive at a computer server according to a Poisson
distribution with a mean rate of 5 per hour.
A. What is the probability that at least three messages will arrive in an
hour?
B. What is the probability that exactly seven messages will arrive during
two hours?
C. What is the probability that the time between two messages will be at
most 10 minutes?
4. The manufacturing of semiconductor chips produces 3% defective
chips. Assume that the chips are independent and that a lot contains 2000
chips. Use the normal approximation to the binomial distribution with the
continuity correction to approximate the probability that a lot has at least
65 defective chips.
5. A synthetic fiber that is used in manufacturing carpet has tensile
strength that is normally distributed with mean 75.5 psi and standard
deviation 4.5 psi. Find the probability that a random sample of n = 9 fiber
specimens will have a sample mean tensile strength that exceeds 76.8 psi
6. A cartridge company develops ink cartridges for a printer company and
supplies both the ink and the cartridges. The following is the probability
mass function of the number of Cartridges used during the life of a
printer.
x
5
6
7
8
9
g(x) .04 .19 .61 .13 .03
A. What is the probability that for seven randomly selected printers at
least five use more than seven cartridges during their life?
B. Consider a random sample of 100 printers. Using the central limit
theorem approximate the probability that a total of at least 710
cartridges are needed?