Statistics Homework 3

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Homework 3 #3

Class Name : MAT2058 Statistics (10wk) - 20200627 - MAT2058 Statistics VB05

Instructor Name : Bibi

Student Name : _____________________ Instructor Note :

Question 1 of 10

Suppose that the New England Colonials baseball team is equally likely to win a game as not to win it. If Colonials games

are chosen at random, what is the probability that exactly of those games are won by the Colonials?

Round your response to at least three decimal places. (If necessary, consult a list of formulas.)

Question 2 of 10

Anita's, a fast-food chain specializing in hot dogs and garlic fries, keeps track of the proportion of its customers who decide to eat in the restaurant (as opposed to ordering the food "to go"), so it can make decisions regarding the possible construction of in-store play areas, the attendance of its mascot Sammy at the franchise locations, and so on. Anita's reports that of its customers order their food to go. If this proportion is correct, what is the probability that, in a

random sample of customers at Anita's, exactly order their food to go?

Round your response to at least three decimal places. (If necessary, consult a list of formulas.)

Question 3 of 10

The following data are the numbers of local channels available in cities.

Construct a box-and-whisker plot for the data.

Question 4 of 10

On each trial of an experiment, a subject is presented with a constant soft noise, which is interrupted at some unpredictable time by a noticeably louder sound. The time it takes for the subject to react to this louder sound is recorded. The following list contains the reaction times (in milliseconds) for the trials of this experiment:

Find th and th percentiles for these reaction times.

(If necessary, consult a list of formulas.)

5 2

45% 5 2

18

21, 6, 38, 25, 27, 13, 16, 15, 21, 26, 31, 12, 8, 31, 12, 17, 33, 39

20

171, 296, 152, 202, 229, 175, 269, 257, 235, 231, 217, 226, 164, 285, 212, 311, 186, 222, 250, 271

25 80

5 10 15 20 25 30 35 Number of local channels available

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Question 5 of 10

Fill in the values to give a legitimate probability distribution for the discrete random variable , whose possible

values are , , , , and .

Value x of X P( X =x )

-5 0.11

-1 0.10

1

4

5 0.23

Question 6 of 10

The following data are the numbers of local channels available in cities.

Construct a box-and-whisker plot for the data.

Question 7 of 10

The following are the annual salaries of chief executive officers of major companies. (The salaries are written in thousands of dollars.)

Find th and th percentiles for these salaries.

(If necessary, consult a list of formulas.)

Question 8 of 10

P =X x X −5 −1 1 4 5

19

40, 21, 30, 11, 12, 26, 38, 25, 11, 21, 28, 12, 16, 27, 6, 31, 24, 23, 30

16

495, 315, 723, 814, 338, 676, 248, 157, 134, 181, 405, 75, 542, 767, 700, 653

25 90

5 10 15 20 25 30 35 Number of local channels available

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Fill in the values to give a legitimate probability distribution for the discrete random variable , whose possible

values are , , , , and .

Value x of X P( X =x )

-4 0.27

3 0.10

4

5

6 0.17

Question 9 of 10

Suppose that the genders of the three children of a certain family are soon to be revealed. Outcomes are thus triples of "girls" ( ) and "boys" ( ), which we write , , etc. For each outcome, let be the random variable counting the

number of boys in each outcome. For example, if the outcome is , then . Suppose that the random variable

is defined in terms of as follows: . The values of are thus:

Outcome

Value of

Calculate the probability distribution function of , i.e. the function . First, fill in the first row with the values of .

Then fill in the appropriate probabilities in the second row.

Value of

Question 10 of 10

The following are the annual salaries of chief executive officers of major companies. (The salaries are written in thousands of dollars.)

Find th and th percentiles for these salaries.

(If necessary, consult a list of formulas.)

P =X x X −4 3 4 5 6

g b gbg bbb R bbb =R bbb 3

X R =X −R2 −2R 4 X

bbg gbb gbg ggb bgg bbb bgb ggg

X −4 −4 −5 −5 −5 −1 −4 −4

X pX x X

x X PX x

18

519, 134, 700, 338, 84, 248, 428, 767, 542, 452, 790, 676, 362, 633, 562, 271, 75, 814

25 60