( You can use any statistical software like Excel, Minitab, SAS, SPSS, Matlab....)

1.The annual number of industrial accidents occurring in a particular manufacturing plant is known to follow a Poisson distribution with mean 12.

a.What is the probability of observing exactly 12 accidents during the coming year?

b.What is the probability of observing no more than 12 accidents during the coming year?

c.What is the probability of observing at least 15 accidents during the coming year?

d.What is the probability of observing between 10 and 15 accidents ( inclusive) duringthe coming year?

e.Find the smallest integer "k" such that we can be at least 99% sure that the annual number of accidents occurring will be less than k.

2.Big Office,a chain of large office supply stores, sells a variety of windows and Mac laptops. Company executives what to know whether the demands for these two types of computers are related in any way. They might act as complementary products, where high demand for Windows laptops accompanies high demand for Mac laptops (computers in general are hot), they might act as substitute products (demand for one takes away demand for the other), or their demands might be unrelated. Because of limitations in its information system, Big Office does not have the exact demands for these products. However, it does have daily information on categories of demand, listed in aggregate (that is, over all stores). Each day's demand for each type of computer is categorized as Low, Medium Low, Medium High or High.From the following data, testwhether demands for Windows laptops is independent of demand for Mac laptops.(Hint: use Chi square ). Test at 5% level of significance

WINDOWS LAPTOPS

Low

Medium

Medium High

High

MAC LAPTOPS

Low

4

17

17

5

Medium

8

23

22

27

High medium

16

20

14

20

High

10

17

19

11

3.Suppose the annual returns on XYZ stock follows a normal distribution with mean 12% and standard deviation 30%.

a.What is the probability that XYZ's value will decrease during a year?

b.What is the probability that the return on XYZ during a year will be at least 20%?

c.What is the probability that the return on XYZ during a year will be between -6% and 9%?

d.There is a 5%chance that the return on XYZ during a year will be greater than what value?

e.There is a 1% chance that the return on XYZ during a year will be less than what value?

f.There is a 95% chance that the return on XYZ during a year will be between which two values (equidistant from the mean)