Question 1:

One of the most profitable items at AI's Auto Security Shop is the remote starting system. Let x be the

number of such systems installed on a given day at this shop. The following table lists the frequency

distribution of x for the past 80 days.

x 1 2 3 4 5

f 8 20 24 16 12

a. Construct a probability distribution table for the number of remote starting systems installed on

a given day.

b. Find the Following probabilities:

I. P(x=3)

II. P(x3)

III. P(2x4)

IV. P(x<4)

Question 2:

Loraine Corporation is planning to market a new makeup product. According to the analysis made by the

financial department of the company, it will earn an annual profit of $4.5 million if this product has high

sales and an annual profit of $ 1.2 million if the sales are mediocre, and it will lose $2.3 million a year if

the sales are low. The probabilities of these three scenarios are .32, .51 and .17 respectively.

a) Let x be the profits (in millions of dollars) earned per annum from this product by the company.

Write the probability distribution of x.

b) Calculate the mean and the standard deviation of x.

Question 3:

Using the Poisson Formula find the following probabilities:

a. P(x1) for =5

b. P(x=2) for =2.5

Question 4:

Let, N=8, r=3 and n=4

Using the Hypergeometric probability distribution formula find the following probabilities:

a. P(x=2)

b. P(x=0)

c. P(x2)