STAT 211 EXAM 1 – FORM A FALL 2004
Samples of six different brands of diet/imitation margarine were analyzed to determine the level of physiologically active polyunsaturated fatty acids (PAPFUA, in percentages), resulting in the following data with 26 observations.
Imperial / Parkay / Blue Bonnet / Chiffon / Mazola / Fleischmann14.1 12.8 13.5 13.2 16.8 18.1
13.6 12.5 13.4 12.7 17.2 17.2
14.4 13.4 14.1 12.6 16.4 18.7
14.3 13.0 14.3 13.9 17.3 18.4
12.3 18.0
The boxplot created for each brand is as follows.
The descriptive statistics for each brand
Imperial / Parkay / Blue Bonnet / Chiffon / Mazola / FleischmannMean / 14.100 / 12.800 / 13.825 / 13.100 / 17.14 / 18.100
Variance / .127 / .185 / .196 / .353 / .358 / .420
Range / .8 / 1.1 / .9 / 1.3 / 1.6 / 1.5
Interquartile Range / .650 / .8 / .825 / 1.100 / 1 .050 / 1.200
Use the given information above to answer the questions 1 to 9.
1. Which of the following can apply to the data?
a) All brands have symmetric data
b) All brands have positively skewed data
c) All brands have negatively skewed data
d) More brands with negatively skewed data than positively skewed
e) More brands with positively skewed data than negatively skewed
2. Only look at the Imperial brand. Which of the following is the median PAPFUA?
a) 13.8
b) 14.0
c) 14.2 the average of 14.1 and 14.3 on the ordered data
d) 14.4
e) None of the above
3. Which brand has the highest variation in the data?
a) Parkay
b) Blue Bonnet
c) Chiffon
d) Mazola
e) Fleischmann looking at standard deviation, range, interquartile range
4. For the Fleischmann brand, which of the following you should use to describe the center of the data?
a) Mean
b) Median it is a skewed data
c) Mode
d) Percentile
e) Quartile
5. Which of the following brands has the mean PAPFUA of 13.825?
a) Parkay
b) Blue Bonnet directly from the descriptive statistics table
c) Chiffon
d) Mazola
e) Fleischmann
6. What proportion of data is not Imperial brand?
a) Approximately 15%
b) Approximately 19%
c) Approximately 81%
d) Approximately 85% 4 observations on the imperial then 22/26
e) Approximately 89%
7. What proportion of data is Blue Bonnet or Chiffon?
a) Approximately 21%
b) Approximately 31% 8 observations out of 26 then 8/26
c) Approximately 41%
d) Approximately 61%
e) Approximately 71%
8. Look at the data with the brands Mazola and Fleischmann only (You have 8 observations). Which of the following is the mode for that data?
a) No mode
b) 16.8
c) 17.2 it is the only repeating observation
d) 18.4
e) 18.7
9. The sample standard deviation for this complete data is 2.132. If each observation in this data set is multiplied by 5, which of the following is the new sample variance?
a) 4.55
b) 10.66
c) 22.73
d) 113.64 new variance=(new standard deviation) 2=[5(2.1232)]2
e) None of the above
10. Which of the following uses the five number summary (minimum, maximum, median, lower and upper quartile) to show the data graphically?
a) Stem and leaf display
b) Histogram
c) Boxplot
d) All of the above
e) None of the above
11. Which of the following should be used on the vertical axis of the histogram for the continuous data with the different interval width?
a) Only frequency
b) Only relative frequency
c) Only density
d) Exactly two of the above
e) All of the measures in (a),(b),(c)
Police report that 78% of drivers stopped on suspicion of drunk driving are given a breath test, 36% a blood test, and 22% both tests. Use this information to answer the questions 12 to 18.
12. Which of the following is the probability that a randomly selected suspect is given test?
a) 0.14
b) 0.56
c) 0.92 =union probability=P(either blood or breath or both tests)=0.78+0.36-0.22
d) 1.14
e) None of the above
13. Which of the following is the probability that a randomly selected suspect is given a breath test not the blood test?
a) 0.14
b) 0.56 =P(breath test)-P(both tests)=0.78-0.22
c) 0.92
d) 1.14
e) None of the above
14. Are giving a suspect a blood test and a breath test mutually exclusive?
a) No because intersection probability is 0.22 not zero.
b) Yes
15. Are giving a suspect a blood test and a breath test independent?
a) No because the intersection probability is not the same as the product of individual prob’s
b) Yes
16. If there are three independently selected suspects, which of the following is the probability of all three have a breath test?
a) 0.0107
b) 0.4746 =(0.78)3
c) 0.5255
d) 0.7800
e) 0.9894
17. If there are three independently selected suspects, which of the following is the probability of breath test is given exactly one of them?
a) 0
b) 0.0378
c) 0.1133 =3(0.78)(1-0.78)2
d) 0.1716
e) 0.4746
18. If there are three independently selected suspects and the breath test has given to exactly one of them, which of the following is the probability of breath test is given to all three of them?
a) 0 exactly one and all three has nothing common
b) 0.0378
c) 0.1133
d) 0.1716
e) 0.4746
A chain of stereo stores is offering a special price on a complete set components (receiver, compact disc player, speakers, cassette deck). A purchaser is offered a choice of manufacturer for each component:
Receiver: Kenwood, Onkyo, Pioneer, Sony, Sherwood
Compact disc player: Onkyo, Pioneer, Sony, Technics
Speakers: Boston, Infinity, Polk
Cassette Deck: Onkyo, Sony, Teac, Technics
Use this information to answer questions 19 to 24:
19. In how many ways can one component of each type is selected?
a) 4 b) 16 c) 240 d) 2056 e) 43680
=5(4)(3)(4)
20. In how many ways can a complete set be selected if the speaker is Boston?
a) 1 b)20 c) 40 d) 60 e) 80
=5(4)(1)(4)
21. In how many ways can a complete set be selected if none is to be Pioneer?
a) 3 b) 12 c) 36 d) 58 e) 144
=4(3)(3)(4)
22. Which of the following is the probability that the complete set selected contains at least one Technics component?
a) 0.0375
b) 0.4375 =1-P(no technics)=1-[5(3)(3)(3)/240]
c) 0.5625
d) 0.9625
e) None of the above
23. Instead of using this special offering, the purchaser will randomly select 12 components (three receiver, three compact disc player, three speakers, and three cassette deck) from all components. In how many ways can those be selected?
a) 4
b) 10
c) 19
d) 160 ==10(4)(1)(4)
e) 240
24. OMITTED
25. Suppose that 23% of adults smoke cigarettes (S). It is known that 57% of smokers and 13% of nonsmokers develop a certain lung condition by age 60 (L). Which of the following is the probability a randomly selected 60-year old has this lung condition?
a) 0.1001
b) 0.1311
c) 0.2312 =P(L|S)P(S)+P(L|no S)P(no S)=0.57(0.23)+0.13(0.77)
d) 0.3313
e) 0.3623