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Variety of Statistical Problems

1. A recent issue of Fortune Magazine reported that the following companies had the lowest sales
per employee among the Fortune 500 companies.

Company
Seagate Technology
SSMC
Russel
Maxxam
Dibrell Brothers

a. How many elements are in the above data set?
5

b. How many variables are in the above data set?

2 - Sales per Employee (1000s) and Sales Rank

c. How many observations are in the above data set?

5 - the same amount of elements that contain these observations. For example, the observation for the element Seagate Technology is $42.20; 285.

d. Name the scale of measurement for each of the variables.
Sales per Employee (1000s) = Interval
Sales Rank = Interval Scale

e. Name the variables and indicate whether they are qualitative or quantitative.

Sales per Employee (1000s) = Quantitative
Sales Rank - Quantitative

2.
Forty shoppers were asked if they preferred the weight of a can of soup to be 6 ounces, 8 ounces, or 10 ounces.
Below are their responses.

6 6 6 10 8 8 8 10 6 6
10 10 8 8 6 6 6 8 6 6
8 8 8 10 8 8 6 10 8 6
6 8 8 8 10 10 8 10 8 6

a. Construct a frequency distribution and graphically represent the frequency distribution.

Frequency Distribution:
Weight (in ounces) Frequency
6 14
8 17
10 9
Total 40

b. Construct a relative frequency distribution and graphically represent the relative frequency distribution.

Weight (in ounces) Frequency Relative Frequency % Frequency
6 14 0.35 35
8 17 0.43 42.5
10 9 0.23 22.5
Total 40 1 100

3.
A sample of 9 mothers was taken. The mothers were asked the age of their oldest child. You are given their responses below.

3 12 4 7 14 6 2 9 11

a. Compute the mean.
7.555555556

b. Compute the variance.
17.77777778

c. Compute the standard deviation.
4.216370214

d. Compute the coefficient of variation.
55.80489989

e. Determine the 25th percentile.
4

f. Determine the median.
7

g. Determine the 75th percentile.
11

h. Determine the range.
12

4.
The sales record of a real estate agency show the following sales over the past 200 days.

Number of Number
Houses Sold of Days
0 60
1 80
2 40
3 16
4 4
200
a. How many sample points are there?
5

b. Assign probabilities to the sample points and show their values.
60/200 = 0.3
80/200 = 0.4
40/200 = 0.2
16/200 = 0.08
4/200 = 0.02
1
c. What is the probability that the agency will not sell any houses in a given day?
60/200 = 0.3

d. What is the probability of selling at least 2 houses?
60/200 = 0.3

e. What is the probability of selling 1 or 2 houses?
80+40 = 120/200 = 0.6

f. What is the probability of selling less than 3 houses?
16+40+80+60 = 196/200 = 0.98

5.
Six viamin and three sugar tablets identical in appearance are in a box. One tablet is taken at random and given to person A.
A tablet is then selected and given to Person B.

What is the probability that n(S) = 9 P(A) = 6/9 =0.666667
n(A) = 6 P(B) = 3/9 = 0..33333
a. Person A was given a vitamin tablet? n(B) = 3
6/9 = 0.666666667

b. Person B was given a sugar tablet given that Person A was given a vitamin tablet?
3/8= 0.38

c. Neither was given vitamin tablets?
3/9= 0.333333333

d. Both were given vitamin tablets?
6/9 = 0.666666667

e. Exactly one person was given a vitamin tablet?
1 / 6 = 0.166666667

f. Person A was given a sugar tablet and Person B was given a vitamin tablet?

6.
The demand for a product varies from month to month. Based on the past year's data, the following probability distribution shows MNM
company's monthly demand.

x F(x) xf(s)
Unit Demand Probability
0 0.10 0(.10) = .00
1000 0.10 1000(.10) = 100
2000 0.30 2000(.30) = 600
3000 0.40 3000(.40) = 1200
4000 0.10 4000(.10) = 400
1.00 2300
a. Determine the expected number of units demanded per month.
2300

b. Each unit produced costs the company $8.00, and is sold for $10.00. How much will the company gain or lose in a month if they stock
the expected number of units dmanded, but sell 2000 units?

2300 x 8 18400 $20,000 - $18,400 = 1600 Loss
2300 x 10 23000
2000 x 8 16000
2000 x 10 20000

7.
a. Define the random variable in words.
A random variable is a numerical description of the outcome of an experiment. The particular numerical value of the random variable depends on the
outcome of the experiment. In this case we have a discrete random variable.

b. The mayor of Daisy City makes $2,250 a month. What percentage of Daisy City's residents has incomes that are more than the mayors?
x = 2250 2250-3000 =-750 / 500 = -1.5
μ = 3000 z = .0668
σ = 500 1-.0668 = 0.9332 93.32%

c. Individuals with incomes of less than $1,985 per month are exempt from city taxes. What percentage of residents is exempt from city taxes?
x = 1,985 1985-3000 = -1015 / 500 = -2.03
μ = 3000 z = .0212
σ = 500 1-.0212 = 0.9788 97.88%

d. What are the minimum and the maximum incomes of the middle 95% of the residents?

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The solution examines a variety of statistics problems. Taxes are examined.

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