Introduction To Probability Models

[Pages:26]Chapter 1. What is Statistics?

1

Practice Final Questions for Statistics 225 Introduction To Probability Models

Material Covered: Chapters 1-7 of Workbook and Text

This is a 2 hour final, worth 25% and marked out of 25 points. The total possible

points awarded for each question is given in square brackets at the beginning of each

question.

Anything

that

can

fit

on

two

sides

of

an

8

1 2

by

11

inch

piece

of

paper

may

be used as a reference during this quiz. A calculator may also be used. No other aids

are permitted.

1. What is Statistics?

(a) One hundred and twenty (120) pea plants are selected at random and the number of pea pods produced per plant is measured (observed). From this group, an average number of pea pods per plant is computed. Match the columns: All of the items in the first column will be used up in the matching procedure; however, one item in the second column will be left unmatched.

statistical terms

(a) value of variable (b) variable (c) parameter (d) population (e) sample (f ) statistic (g) sample size

pea pods example

(a) average number of pea pods per plant for 120 pea plants (b) all pea plants (c) number of pea pods per plant for all pea plants (d) number of pea pods for a pea plant (e) average number of pods per plant for all pea plants (f ) 120 (g) number of pea pods per plant for 120 pea plants (h) number of pea pods for a particular pea plant

terms

(a)

(b)

(c)

(d)

(e)

(f )

(g)

pea pod example

(b) Assume measurements for Ph levels in soil follow exactly a normal relative frequency distribution with population mean = 5 and population standard deviation = 1.4. Use Empirical rule to determine percentage of Ph levels in interval 3.6 to 6.4 (choose one).

(i) 0.68 (ii) 0.78 (iii) 0.95 (iv) 0.99 (v) 0.995

Chapter 2. Probability

2

2. Probability

(a) [1 point] Describe sample space associated with flipping a coin until either heads or tails occurs twice. Choose one.

(i) {, , , , , } (ii) {, , , , , } (iii) {, , , , , } (iv) {, , , , , } (v) {, , , , , }

(b) [1 point] Number of four?digit numbers that can be formed from digits 1, 2 and 3, if each four?digit number must be odd is (choose one)

(i) 27 (ii) 35 (iii) 44 (iv) 54 (v) 67

(c) [1 point] In two rolls of a fair die, let event be the event that no fours, fives or sixes are rolled. Then, () = (choose one)

(i)

8 36

(ii)

9 36

(iii)

10 36

(iv)

11 36

(v)

13 36

(d) [1 point] Let and be two events of an experiment where () = 0.35, ( ) = 0.15 and ( ) = 0.03. Then (? ? ) =

(i) 0.96 (ii) 0.97 (iii) 0.98 (iv) 0.99 (v) 1.00

Chapter 2. Probability

3

(e) [1 point] A survey was conducted comparing age with number of visits per year to doctor. One person is chosen at random.

visits

age 1 to 3 4 to 8 9 to 11 column totals

youth 70 130 90 290

middle?aged 95 450 30 575

elderly 35 30 70 135

row totals 200 610 190 1000

Chance person is a youth, given s/he makes 4?8 visits is (choose closest one):

(i) 0.112 (ii) 0.130 (iii) 0.183 (iv) 0.213 (v) 0.303

(f ) [1 point] Two tickets drawn at random without replacement from following box.

1 2 1 3 2 3

Probability first ticket is a "1" and second card is a "2" is (choose closest one)

(i) 0.1333 (ii) 0.2163 (iii) 0.2566 (iv) 0.3777 (v) 0.4333

(g) [1 point] Urn A has 10 red and 9 blue marbles; urn B has 10 red and 10 blue marbles. A fair coin is tossed. If coin comes up heads, a marble from urn A is chosen, otherwise a marble from urn B is chosen. Chance coin is flipped heads given a red marble is chosen is (choose closest one)

(i)

17 39

(ii)

18 39

(iii)

19 39

(iv)

20 39

(v)

21 39

Chapter 3. Discrete Random Variables and Their Probability Distributions

4

3. Discrete Random Variables and Their Probability Distributions

(a) [1 point] Number of sales of household appliances, , Whirlpool representative Darlene makes in a day is given by following probability distribution.

012345

() 0.10 0.28 0.18 0.11 0.16 0.17

Expected number of sales she makes is (choose closest one):

(i) 0.41 (ii) 1.45 (iii) 2.46 (iv) 3.45 (v) 3.76

(b) [1 point] Number of sales of household appliances, , Whirlpool representative Darlene makes in a day is given by following probability distribution.

012345

() 0.10 0.28 0.18 0.11 0.16 0.17

Standard deviation in number of sales she makes is (choose closest one):

(i) 0.37 (ii) 0.40 (iii) 1.66 (iv) 2.75 (v) 3.76

(c) [1 point] If ( ) = 6, then (2 - 4) = (choose one)

(i) 8 (ii) 16 (iii) 20 (iv) 24 (v) 32

Chapter 3. Discrete Random Variables and Their Probability Distributions

5

(d) [1 point] On a multiple choice exam with 5 possible answers for each of 10 questions, what is probability a student gets 8 or more correct answers just by guessing? Choose closest one. [Hint: binomial.]

(i) 5.7926 ? 10-5 (ii) 6.7926 ? 10-5 (iii) 7.7926 ? 10-5 (iv) 8.7926 ? 10-5 (v) 9.7926 ? 10-5

(e) [1 point] There is a 43% chance of making a basket on a free throw and each throw is independent of each other throw. What is expected number of throws to make first basket? Choose one. [Hint: geometric.]

(i) 2.33 (ii) 4.65 (iii) 6.11 (iv) 8.39 (v) 10.42

(f ) [1 point] There is a 95% chance of passing any exam. What is variance in number of attempts until third exam is passed? Choose closest one. [Hint: negative binomial.]

(i) 0.146 (ii) 0.156 (iii) 0.166 (iv) 0.176 (v) 0.186

(g) [1 point] Eight journalists randomly picked from a pack of 240 of which 15 are also photographers. Chance 3 of 8 picked are photographers is (choose one)

( )(

)

8 232

( )(

)

15 225

(i)

3(

5)

240

(ii)

3(

)5

225

( 8)(

)

15 225

( 8)( ) 15 5

(iv)

5(

)3

240

(v)

3( )5 15

8

8

( )(

)

15 225

(iii)

3(

)5

240

8

Chapter 3. Discrete Random Variables and Their Probability Distributions

6

(h) [1 point] Average of = 7 particles hit a magnetic detection field per microsecond. What is probability at most 5 particles hit in one microsecond? Choose closest one. [Hint: poisson.]

(i) 0.231 (ii) 0.254 (iii) 0.273 (iv) 0.293 (v) 0.301

(i) [1 point] Identify the moment generating function

(i) binomial, = 4 (ii) binomial, = 4 (iii) geometric, = 4 (iv) geometric, = 4 (v) poisson, = 4

()

=

1

1 4

-

3 4

.

(j) [1 point] According to Tchebysheff's Theorem, if = 2 and = 0.5 for random variable , then (1 < < 3) where = (choose one)

(i) 0.75 (ii) 0.80 (iii) 0.85 (iv) 0.90 (v) 0.95

Chapter 4. Continuous Variables and Their Probability Distributions

7

4. Continuous Variables and Their Probability Distributions

(a) [1 point] Let be a continuous random variable where

{

() =

+ 5 if 0 10

0

otherwise

Then constant is (choose one)

(i)

-

47 50

(ii)

-

48 50

(iii)

-

49 50

(iv)

-

50 50

(v) does not exist

(b) [1 point] Let be a continuous random variable where

{

() =

1

if -3 15

0 otherwise

Then constant = (choose one)

(i) 3 (ii) 9 (iii) 12 (iv) 15 (v) 18

(c) [1 point] Let be a continuous random variable where

{1

() =

18

0

if -3 15 otherwise

Then, for -3 15, distribution () =

(i)

-3 18

(ii)

15

(iii)

-3 15

(iv)

18

(v)

+3 18

Chapter 4. Continuous Variables and Their Probability Distributions

8

(d) [1 point] Let be a continuous random variable where

0,

()

=

+3 18

,

1,

< -3, -3 < 15, 15.

(-2 < < 9) (choose closest one)

(i) 0.61 (ii) 0.68 (iii) 0.73 (iv) 0.79 (v) 0.81

(e) [1 point] Let be a continuous random variable where

{1

() =

18

0

if -3 15 otherwise

Then expected value = (choose closest one)

(i) 3 (ii) 6 (iii) 9 (iv) 15 (v) 18

(f ) [1 point] Let be a continuous random variable where

{1

() =

18

0

if -3 15 otherwise

Then variance 2 = (choose closest one)

(i) 23 (ii) 24 (iii) 25 (iv) 26 (v) 27

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