1 Oriental Reproductions Inc is a company that produces hand

1. Oriental Reproductions, Inc. is a company that produces handmade carpets with oriental
designs. The production records show that the monthly production has ranged from 1 to 5
carpets. The production levels and their respective probabilities are shown below.
Production per
month (x)
Probability
1
2
3
4
5
0.01
0.04
0.10
0.80
0.05
Calculate the expected monthly production level and the standard deviation for the
production. Show mathematical detail to receive full credit. You will receive a zero
just for providing the final answer.
2. In a large corporation, 65% of the employees are male. A random sample of five
employees is selected. Use the Binomial probability tables to answer the following
questions. Show mathematical detail to receive full credit. You will receive a zero
just for providing the final answer.
a. What is the probability that the sample contains exactly three male employees?
b. What is the probability that the sample contains no male employees?
c. What is the probability that the sample contains more than three female employees?
d. What is the expected number of female employees in the sample?
3. On the average, 6.7 cars arrive at the drive-up window of a bank every hour. Define the
random variable X to be the number of cars arriving in any hour. Show mathematical
detail to receive full credit. You will receive a zero just for providing the final
answer.
a. What is the appropriate probability distribution for X?
b. Compute the probability that exactly 5 cars will arrive in the next hour.
c. Compute the probability that no more than 5 cars will arrive in the next hour.

Solution

. On the average, 6.7 cars arrive at the drive-up window of a bank every hour. Define the
random variable X to be the number of cars arriving in any hour. Show mathematical
detail to receive full credit. You will receive a zero just for providing the final
answer.
a. What is the appropriate probability distribution for X?
b. Compute the probability that exactly 5 cars will arrive in the next hour.
c. Compute the probability that no more than 5 cars will arrive in the next hour.

a. This is a Poisson distribution. The Poisson distribution is defined by an average number of events over a particular period in time or space. In this case, the period is one hour and the average is 6.7

b. Using Excel:

p(x = 5)
=POISSON(5,6.7,FALSE)
0.1385


c.

Using Excel:

p(x <= 5)
=POISSON(5,6.7,TRUE)
0.3406