Question one.
a) The number of connections on the internet during two-minute period is given by the following
distribution
Number of times
Proportion
i.
ii.
0
0.1
1
0.2
2
0.1
3
0.4
4
0.2
Determine the mean number of times a connection is made during a two-minute
period
ii. Determine the standard deviation of the number of times a connection is made
during a two-minute period
b) Abdullah is considering an investment in a company. He is interested in buying a number of
shares of this company and keeps them for one year. The price of a single share at this time is
$16 and the forecasted price a year from today is given in the following table
Price of stock in one year
Probability
i.
ii.
15
0.15
16
0.20
17
0.26
18
0.21
19
0.18
Does the information above describe a valid probability distribution function? Justify
ii. What is the variance and standard deviation of the stock price a year from today?
C) A packing company is inspecting a shipment of grapefruit by cutting 15 grapefruit selected at
random. The company will accept all grapefruit if 14 or all of these 15 grapefruit are of
satisfactory quality. Suppose that 95% of the grapefruit of the shipment are of satisfactory
quality.
i.
ii.
Write the probability distribution of the grapefruits that are of satisfactory quality in the
sample of 15 grapefruit.
What is the probability that the shipment will be accepted? (I.e. the probability of 14 or
15 good grapefruits out of 15)?
d) A bag contains 7 English books and 5 Math books. Suppose that you randomly select 4 books
from the bag. Let X is the number of Math books in these 4 books that will be selected from the
bag.
i.
ii.
Write the probability distribution of X?
What is the probability that you select two Math and two English books?
e) Esther must select two Management courses and 3 Math courses. If the catalog contains 5
management and 8 Math courses, how many ways can Esther complete her schedule?