*label*Science

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β’

β’

On questions requiring a numerical answer, show how the answer was obtained by

Excel files.

Answer all sub questions (if any) of a problem for full credit for that problem.

Exercise 3-95 on Page 101

Customers purchase a particular make of automobile with a variety of options. The

probability mass function of the number of options is

x

7

8

9

10

11

12

13

π(π₯)

0.040

0.130

0.190

0.240

0.300

0.050

0.050

(a) What is the probability that a customer will choose fewer than 9 options?

P(7)+P(8) = 0.040 + 0.130 = 0.17

(b) What is the probability that a customer will choose more than 11 options?

P(12)+P(13) = 0.050 + 0.050 = 0.1

(c) What is the probability that a customer will choose between 8 and 12 options,

inclusively?

P(8)+P(9)+P(10)+P(11)+P(12) = 0.91

(d) What is the expected number of options chosen? What is the variance?

E(X)=7(.04)+8(.13)+9(.19)+10(.24)+11(0.3)+12(.05)+13(.05) = 9.98

Var(x) = β7π=1 π(π₯π )(π₯π β 9.98)2 = 2.0196

Exercise 3-130 on page 117

Flaws occur in Mylar material according to a Poisson distribution with a mean of 0.01 flaw

per square yard.

(a) If 25 square yards are inspected, what is the probability that there are no flaws?

P(0, .25) =

π β.25 .250

0

= 0.77880078

(b) What is the probability that a randomly selected square yard has no flaws?

P(0,0.01) =

π β0.01 0.010

0!

=.99004983

(c) Suppose that the Mylar material is cut into 10 pieces, each being 1 yard square.

What is the probability that 8 or more of the 10 pieces will have no flaws? Hint:

Let V denote the number of square ...

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