Assignment 20%

1. State the level of measurement for each of the following variables:a. Students grade point averages (CGPA) = Ratio levelb. Distance students travel to class = Ratio levelc. Student scores on the first statistics test = Ratio leveld. A classification of students by state of birth = Ordinal levele. A ranking of students by freshman, sophomore, junior and senior = Ordinal levelf. Number of hours students study per week = Ratio level

2. The local manager of Food queen is interested in number of times a customer shops at her store during a two-week period. The responses of 51 customers were:

5 3 3 1 4 4 5 6 4 2 6 6 6 7 1 1 9

1 14 1 2 4 4 4 5 6 3 5 3 4 5 6 10 2

8 4 7 6 5 9 11 3 12 4 7 6 5 15 1 8 12

a. Starting with 0 the lower limit of the first class and using class interval of 3, organize the data into frequency distribution

Classes Frequency

0 – 3 14

4 – 7 27

8 – 11 6

12 – 15 4

b. Describe the distribution. Where do the data tend to cluster?The data tend to cluster at 4 – 7 classes.

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c. Convert the distribution to a relative frequency distribution.

Classes Relative frequency

0 – 3 0.2745

4 – 7 0.5294

8 – 11 0.1177

12 – 15 0.0780

d. Calculate the cumulative frequency distribution.

Classes Cumulative frequency

0 – 3 14

4 – 7 41

8 – 11 47

12 – 15 51

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3. The Marketing Research Department is investigating the performance of several corporations in the coal, mining and gas industries. The fourth-quarter sales in 1997 ( in millions of dollars) for the corporations are:

Corporation Fourth-Quarter Sales ($millions)

American Hess 1645.3

Atlantic Richfield 4757

Chevron 8913

Diamond Shamrockon 627.1

Exxon 24612.0

Quarker State 191.9

The Department wants to include a chart in their report comparing the fourth- quarter sales of the six corporations. Use a bar chart to compare the fourth-quarter sales of these corporations and write a brief report summarizing the bar chart.

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Report: Exxon has highest value of Fourth-Quarter Sales but Quaker State has lowest Fourth-Quarter Sales.

4. A sample of households that subscribe to the United Bell Phone Company revealed the following numbers of calls received last week. Determine the mean and the median number of calls received.

52 43 30 38 30 42 12 3934 46 32 18 41 5 46 37

Mean:

X= fx n

52+34+43+46+30+32+38+18+30+41+42+5+12+46+39+37 = 545 16 16

=34.0625

Median:

5, 12, 18, 30, 30, 32, 34, 37, 38, 39, 41, 42, 43, 46, 46, 52

37+38 = 37.5 2

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5. A major airline wanted some information on those enrolled in their “frequent flyer” program. A sample of 48 members resulted in the following numbers of miles flown, to the nearest 1,000 miles, by each participant. Develop a dot plot of the data and comment on the information

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22 29 32 38 39 41 42 43 43 43 44 44

45 45 46 46 46 47 50 51 52 54 54 55

56 57 58 59 60 61 61 63 63 64 64 67

69 70 70 70 71 71 72 73 74 76 78 88

6. The following data are the estimated values (in $million) of 50 companies in the auto parts business.

26.8 8.6 6.5 30.6 15.4 18.0 7.6 21.5 11.0 10.2

28.3 15.5 31.4 23.4 4.3 20.2 33.5 7.9 11.2 1.0

11.7 18.5 6.8 22.3 12.9 29.8 1.3 14.1 29.7 18.7

6.7 31.4 30.4 20.6 5.2 37.8 13.4 18.3 27.1 32.7

6.1 0.9 9.6 35.0 17.1 1.9 1.2 16.6 31.1 16.1

a. Determine the mean and median of the market values.

Mean:=Σx

N

=857.9 = 17.16 50

Median:

0.9, 1.0, 1.2, 1.3, 1.9, 4.3, 5.2, 6.1, 6.5, 6.7, 6.8, 7.6, 7.9, 8.6, 9.6, 10.2, 11.0, 11.2, 11.7, 12.9, 13.4, 14.1, 15.4, 15.5, 16.1, 16.6, 17.1, 18.0, 18.3, 18.5, 18.7, 20.2, 20.6, 21.5, 22.3, 23.4, 26.8, 27.1, 28.3, 29.7, 29.8, 30.4,

30.8, 31.1, 31.4, 31.4, 32.7, 33.5, 35.0, 37.8.

16.1+16.6 = 16.35 2

b. Determine the standard deviation of the marker values.

S=√(∑(x- )2/ (n-1))

Each X (the data has been ∑(x- )2)

S=√5486.88/496

S=10.58

c. Using Chebyshev’s theorem, between what values would you expect about 56 percent of the market values occur?

1-1/k2 x 100

1-1/k2 x 100 = 561-1/k2 = 0.561-0.56=1/k2

0.44=1/k2

k2 = 1/0.44k2 = 2.27k = 1.51

17.16-(1.51)(10.58)=1.18

17.16+ (1.51)(10.58)=33.14

The values are between 1.18 to 33.14

d. Using the Empirical rule, about 95% of the values would occur between what values?

95% that is k=2

17.16- (2)(10.58)=-4

17.16 + (2)(10.58)=38.32

The values are between -4 to 38.32

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e. Determine the coefficient of variation.

CV= (s/ )x 100CV= (10.58/17.16)x100CV= 61.66% f. Determine the coefficient of skewness.

Skewness = (3( - M)) / 5Skewness = (3(17.16-16.35)) / 5Skewness = 0.2298

It is positively skew.

g. Estimate the values of the first and the third quartile.

Lp = (n+1)p/100

Q1

L25=(50+1)25/100 =(51)25/100 =12.75

It is between 12th to 13th.

12.75-12=0.757.9-7.6=0.30.3x0.75=0.2257.6+0.225=7.825Q1=7.825

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Q3

L75=(50+1)75/100 =(51)75/100 =38.25

It is between 38th to 39th.

38.25-38=0.2528.3-27.1=1.21.2x0.25=0.327.1+0.3=27.4Q3=27.4

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7. In each of the following cases, indicate whether classical, empirical or subjective probability is used.

a. A basketball player makes 30 out of 50 foul shots. The probability is 0.6 that she makes the next foul shot attempted.

=Empirical

b. A seven-member committee of students is formed to study environmental issues. What is the likelihood that any one of the seven is chosen as the spokesperson?

=Classical

c. You purchase one of 5 million tickets sold for Lotta Canada. What is the likelihood you win the $1 million jackpot?

=Subjective

d. The probability of an earthquake in Northern California in the next 10 years is 0.80. =Subjective

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8. A study of 200 grocery chains revealed these incomes after taxes:

Incomes after Taxes Number of Firms

Under $1 million 102

$1 million to $20 million 61

$20 million or more 37

a. What is that a particular chain has under $1 million in income after taxes?

P(under $1 million)= 102/200 = 0.51

b. What is the probability that a grocery chain selected at random has either an income between $1 million and $20 million, or an income of $20 million or more? What rule of probability was applied?

P($1 million and $20 million U $20 million or more) = P($1 million and $20 million) + P($20 million or more)=61/200 + 37/200=0.49

Additional rule.

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9. A hospital administrator is looking over the Knox County Medical Society survey of its members, which is records their gender and age. The following table summarizes the results:

Gender Under 35 Between 35 and 54

Over 54 Total

Male 27 87 26 140

Female 14 25 3 42

Total 41 112 29 182

If you randomly select a member of the society, what is the probability they are:

a. Male?

P(male)=140/182=10/13 =0.7692

b. Between the ages of 35 and 54?

P(Between the ages of 35 and 54)=112/182=8/13 =0.6154

c. Both male and between the ages of 35 and 54?

P(male ∩ between the ages of 35 and 54)=P(male) x P(between the ages of 35 and 54) =140/182 x 87/140 =87/182 =0.4780

d. Both female and over 54?

P(female ∩ over 54)= P(female) x P(over 54) =42/182 x 3/42 =3/182 =0.01648

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e. Either male or between the ages of 35 and 54?

P(male U between the ages of 35 and 54)=P(male) + P(between the ages of 35 and 54) – p(male ∩ between the ages of 35 and 54)=140/182 + 112/182 – 87/182=165/182=0.9066 f. Either female or over 54?

P(female U over 54)= P(female)+P(over 54) - P(female ∩ over 54) =42/182 + 29/182 – 3/182 =74/182 =0.4066

g. Male, given that they are under 35?

P(male, under 35)=27/140 =0.1929

h. Male, given that they are over 54?

P(male, over 54)=26/140=13/70 =0.1857

i. Over 54, given that they are male?

P(over 54, male)=26/29 =0.8966

j. Over 54. Given that they are female?

P(over 54, female)=3/29 =0.1034

k. Are the events “male” and “between the ages of 35 and 54” independent?13

=No

l. Are the events “female” and “over 54” independent?

=No

m. Are the events “male” and “over 54” mutually exclusive?

=No

n. Are the events “female” and “male” mutually exclusive?

=Yes

10. A national pollster has developed 15 questions designed to rate the performance of the president of the United States. The pollster will select 10 of these questions. How many different arrangements are there for the order of the 10 selected questions?

15P10 = ___15!__ (15-10)!

= 15x14x13x12x11x10x9x8x7x6 x5x4x3x2x1 5x4x3x2x1

=10897286400

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