Mathematics
Problem 1
You wish to determine the GPA of students at your school. Describe whatprocess you would go through to collect a sample if you use a systematic sample.
Problem 2
The number of deaths in the US due to carbon monoxide (CO) poisoning fromgenerators from the years 1999 to 2011 are in table #1 (Hinatov, 2012).
Create a bar chart and pie chart of this data. State any findings you see from the graph.
Table #1: Data of Number of Deaths Due to CO Poisoning
Region |
Number of deaths from CO while using a generator |
Urban Core |
401 |
Sub-Urban |
97 |
Large Rural |
86 |
Small Rural/Isolated |
111 |
Problem 3
The density of people per square kilometer for African countries is in table#2 (“Density of people,” 2013).
a.) Create a frequency distribution, relativefrequency distribution, and cumulative frequency distribution using 8 classes.
b.) Create a histogram for the data in table #2.Describe the shape and any findings you can from the graph.
c.) Create an ogive for the data in table #2. Describe any findings you can from the graph.
Table #2: Data of Density of People per Square Kilometer
15 |
16 |
81 |
3 |
62 |
367 |
42 |
123 |
8 |
9 |
337 |
12 |
29 |
70 |
39 |
83 |
26 |
51 |
79 |
6 |
157 |
105 |
42 |
45 |
72 |
72 |
37 |
4 |
36 |
134 |
12 |
3 |
630 |
563 |
72 |
29 |
3 |
13 |
176 |
341 |
415 |
187 |
65 |
194 |
75 |
16 |
41 |
18 |
69 |
49 |
103 |
65 |
143 |
2 |
18 |
31 |
Problem 4
The World Bank collects information on the life expectancy of a person in eachcountry (“Life expectancy at,” 2013) and the fertility rate per woman in thecountry (“Fertility rate,” 2013). The data for 24 randomly selected countries forthe year 2011 are in
table #3. Create a scatter plot of the data and state if thereappears to be a relationship between life expectancy and the number of births perwoman.
Table #3: Data of Life Expectancy versus Fertility Rate
Life |
Fertility |
Life |
Fertility |
77.2 |
1.7 |
72.3 |
3.9 |
55.4 |
5.8 |
76.0 |
1.5 |
69.9 |
2.2 |
66.0 |
4.2 |
76.4 |
2.1 |
55.9 |
5.2 |
75.0 |
1.8 |
54.4 |
6.8 |
78.2 |
2.0 |
62.9 |
4.7 |
73.0 |
2.6 |
78.3 |
2.1 |
70.8 |
2.8 |
72.1 |
2.9 |
82.6 |
1.4 |
80.7 |
1.4 |
68.9 |
2.6 |
74.2 |
2.5 |
81.0 |
1.5 |
73.3 |
1.5 |
54.2 |
6.9 |
67.1 |
2.1 |
Problem 5
Cholesterol levels were collected from patients two days after they had a heartattack (Ryan, Joiner & Ryan, Jr, 1985) and are in table #4. Find the mean,median, range, variance, and standard deviation using technology.
Table #4: Cholesterol Levels
270 |
236 |
210 |
142 |
280 |
272 |
160 |
220 |
226 |
242 |
186 |
266 |
206 |
318 |
294 |
282 |
234 |
224 |
276 |
282 |
360 |
310 |
280 |
278 |
288 |
288 |
244 |
236 |
Problem 6
Eyeglassomatic manufactures eyeglasses for different retailers. They test to seehow many defective lenses they made in a time period. Table #5 gives thedefect and the number of defects.
Table #5: Number of Defective Lenses
Defect type |
Number of Defects |
Scratch |
5865 |
Right shaped – small |
4613 |
Flaked |
1992 |
Wrong axis |
1838 |
Chamfer wrong |
1596 |
Crazing, cracks |
1546 |
Wrong shape |
1485 |
Wrong PD |
1398 |
Spots and bubbles |
1371 |
Wrong height |
1130 |
Right shape – big |
1105 |
Lost in lab |
976 |
Spots/bubble – intern |
976 |
a.) Find the probability of picking a lens that is scratched or flaked.
b.) Find the probability of picking a lens that is the wrong PD or was lost in lab.
c.) Find the probability of picking a lens that is not scratched.
d.) Find the probability of picking a lens that is not the wrong shape.
Problem 7
According to an article in the American Heart Association’s publicationCirculation, 24% of patients who had been hospitalized for an acute myocardialinfarction did not fill their cardiac medication by the seventh day of beingdischarged (Ho, Bryson & Rumsfeld, 2009). Suppose there are twelve peoplewho have been hospitalized for an acute myocardial infarction.
a.) State the random variable.
b.) Argue that this is a binomial experiment
Find the probability that
c.) All filled their cardiac medication.
d.) Seven did not fill their cardiac medication.
e.) None filled their cardiac medication.
f.) At most two did not fill their cardiac medication.
Problem 8
The mean starting salary for nurses is $67,694 nationally (“Staff nurse -,” 2013).The standard deviation is approximately $10,333. Assume that the starting salaryis normally distributed.
a.) State the random variable.
b.) Find the probability that a starting nurse will make more than $80,000.
c.) Find the probability that a starting nurse will make less than $60,000.
d.) If a nurse made less than $50,000, would you think the nurse was under paid?
Why or why not?
Problem 9
The WHO MONICA Project collected blood pressure data for people in China
(Kuulasmaa, Hense&Tolonen, 1998). Data based on information from the study is in table #6. Determine if the data is from a population that is normallydistributed.
Table #6: Blood Pressure Values for People in China
114 |
141 |
154 |
137 |
131 |
132 |
133 |
156 |
119 |
138 |
86 |
122 |
112 |
114 |
177 |
128 |
137 |
140 |
171 |
129 |
127 |
104 |
97 |
135 |
107 |
136 |
118 |
92 |
182 |
150 |
142 |
97 |
140 |
106 |
76 |
115 |
119 |
125 |
162 |
80 |
138 |
124 |
132 |
143 |
119 |
Problem 10
The size of fish is very important to commercial fishing. A study conducted in2012 found the length of Atlantic cod caught in nets in Karlskrona to have a meanof 49.9 cm and a standard deviation of 3.74 cm (Ovegard, Berndt &Lunneryd, 2012). The length of fish is normally distributed. A sample of 15 fish is taken.
a.) State the random variable.
b.) Find the mean and standard deviation of the sample mean.
c.) Find the probability that the sample mean length of the Atlantic cod is lessthan
52 cm.
d.) Find the probability that the sample mean length of the Atlantic cod is morethan
74 cm.
e.) If you found sample mean length for Atlantic cod to be more than 74 cm, whatcould you conclude?
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