Question

1. Based on the information, please compute the following measures:

Daily Supply (y)	Unit Price (x)
15	11
13	12
17	15
19	8
16	9

(1) Mean for variable y and for x.

(2) Standard deviation for variable y and for variable x. (Please show the detail computation steps. Please don’t just give an answer from Excel functions or calculator functions. Otherwise, you will not get all the points.)

[Hint: (Please see Slide 26 of Chapter 3 for formula). Please also see related materials in the textbook.)]

2. You are given the following information on Events A, B, C, and D.

P(A) =0.43   P(A ⋃ C) =0.6

P(B) =0.25   P(A | B) =0.2

P(D) =0.35 P(A ∩ C) =0 .04 P(A ∩ D) =0 .05

Please do the following:

a.       Compute P(C).

b.       Compute P(A ∩ B).

c.       Compute P(A | D).

c.       Compute P(D | A).

Hint: [Please see Chapter 4 – Slides 22 - 23 for definition of union of events, see Slides 24 - 25 for definition of intersection of events, and Slide 26 for Addition Law.]

3. As a company manager for Claimstat Corporation there is a 0.40 probability that you will be promoted this year. There is a 0.6 probability that you will get a promotion, a raise, or both. The probability of getting a promotion and a raise is 0.3.

(1) If you get a raise, what is the probability that you will also get a promotion?

(2) Are getting a raise and being promoted independent events? Explain using probabilities.

(3) Are these two events mutually exclusive? Explain using probabilities.

Answer 1

• Calculations for s.d ( y )

data	data-mean	(data - mean)2
15	-1	1
13	-3	9
17	1	1
19	3	9
16	0	0

Find the sum of numbers in the last column to get.

∑(yi− y bar)²=20

• Calculations for s.d ( x)

Create the following table.

data	data-mean	(data - mean)2
11	0	0
12	1	1
15	4	16
8	-3	9
9	-2	4

Find the sum of numbers in the last column to get.

∑(xi−X bar)²=30