1. If the random variable z is the standard normal score and P(z 0. Why or why not? (Points : 3) 2. Given a binomial distribution with n = 20 and p = 0.76, would the normal distribution provide a...

1. (A) Classify the following as an example of nominal, ordinal, interval, or
atio level of measurement, and state why it represents this level: eye color
Answer:
Eye color is nominal scale. This is because it has no order and there is no
distance between YES and NO.
(B) Determine if this data is qualitative or quantitative: weight
Answer:
The data are quantitative because weights can be measured in numbers.
(C) In your own line of work, give one example of a discrete and one example
of a continuous random variable, and describe why each is continuous or
discrete. (Points : 9)
Answer:
Example of discrete random variable; number of cars. This is discrete random
variable because this variable will always take a discrete value.
Example of continuous variable; height. This is a continuous random variable
ecause height can take any value i.e. it can be represented in fractions.
2. A construction company ordered a variety of lumber grades for their new
housing developments for the purpose of examining characteristics of
durability and longevity of their construction projects. The company
ecorded durability and longevity data on each development over a period of
five years. At the end of the five years, they reported the results of their
esearch to all construction organizations through a national publication.
I. What is the population?
Answer:
Population is all housing developments completed so far.

II. What is the sample?
Answer:
Sample is durability and longevity data on each development over a period of
five years.

III. Is the study observational or experimental? Justify your answer.
Answer:
The study is observational. This is because, the data has been collected
after the project is complete and has been collected for over the period of
time.

IV. What are the variables?
Answer:
Variables are; durability and longevity, lumber grades

V. For each of those variables, what level of measurement (nominal, ordinal,
interval, or ratio) was used to obtain data from these variables? (Points : 12)
Answer:
Durability and longevity has been measured on ordinal scale
lumber grades has been measured in interval scale because it is a ordered
anking.
3. Construct both an ungrouped and a grouped frequency distribution for the
data given below:
92 93 86 81 85 81 86 88 89 93
83 92 81 93 92 85 93 82 95 86 (Points : 10)
Answer:
Ungrouped:
Observation Frequency
81 3
82 2
83 1
85 2
86 2
88 1
89 1
92 3
93 4
95 1
Grouped:
Class
interval frequency
80-85 6
85-90 6
90-95 7
95-100 1
4. Given the following frequency distribution, find the mean, variance, and
standard deviation. Please show all of your work.
Class Frequency
51-53 7
54-56 19
57-59 9
60-62 13
63-65 15

Answer:
Class
Frequency
(f)
X (mid
value)
fX (X-58.48) (X-58.48)^2 [(X-58.48)^2]*f
51-53 7 52 364
-
6.476190476
41.94104308 293.5873016
54-56 19 55 1045
-
3.476190476
12.08390023 229.5941043
57-59 9 58 522
-
0.476190476
0.22675737 2.040816327
60-62 13 61 793 2.523809524 6.369614512 82.80498866
63-65 15 64 960 5.523809524 30.51247166 457.6870748
Total 63 3684 1065.714286

Mean = ∑ ∑ = 3684/63 = 58.48
Variance = ∑ /∑ = 1065.714286/63 = 16.92
Standard deviation = √ = (16.92)^(1/2) = 4.11
5. The following data lists the average monthly snowfall for...