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Name___________________________
MA 225 :
Test 1
I.
Multiple choice/Short Answers: 20 points
1. A histogram that is negatively skewed is
A.
B.
C.
D.
2.
skewed to the right
skewed to the left
a histogram with exactly two peaks
symmetric
Which of the following statements are false?
A. A physical interpretation of the sample mean x demonstrates how it measures the
location (center) of a sample.
B. The sample median, represented by x, is the middle value when the observations
are ordered from smallest to largest.
C. The sample median is very sensitive to extremely small or extremely large data
values (outliers).
D. The sample mean is very sensitive to extremely small or extremely large data values
(outliers).
3.
Which of the following statements are true?
A. The unit for the standard deviation is the same as the unit for the data values.
B. The average deviation of x1 , x2 ,....., xn from the mean x may be positive or
negative.
C. The average absolute deviation of
D. We use 
variance.
4.
2
x1 , x2 ,....., xn from the mean x is always zero.
(square of the lowercase Greek letter sigma) to denote the sample
For a sample of size 5, if
x1  x  5, x2  x  9, x3  x  7,and x4  x  2, then the
sample standard deviation is
A.
B.
C.
D.
5.
5.639
6.782
6.066
6.305
Given that n =10,
A.
B.
C.
E.
x
i
 25, and  xi = 512, then the sample standard deviation is
2
7.012
6.704
7.067
None of the above answers is correct
1
6.
Which of the following statements are correct if
yx
A.
B.
y  x 5
C.
s y2  sx2  5
D. sy2  sx2  25
F. None of the above
7.
Which of the following statements are correct if
A.
B.
y  2x
y  4x
C.
sy2  2sx2
D. sy2  sx2  4
8.
Boxplots have been used successfully to describe
A.
B.
C.
D.
E.
center of a data set
spread of a data set
the extent and nature of any departure from symmetry
identification of “outliers”
All of the above
9. Joe Fafatone wants to buy a particular TiVo unit.. Being a known cheapskate, Joe decides to
monitor prices over a 15 week period. He has compiled the following information:
Mean Price
Standard Deviation
Best Buy
324.00
15.28
Circuit City
320.00
4.18
If Joe is really looking for a bargain, where should he shop______________
Why________________________
10. Fill in the caption of the cartoon with the appropriate measure of central tendency:
“Should we scare the other team by announcing our _____ height or lull them by announcing
our _______ height.”
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II. Consider the following information: where A = {Visa Card}, B = {MasterCard}, P(A) = .5, P(B) =
.4, and P(A  B) = .25. Calculate each of the following probabilities. (15 points)
a. P(B|A)
b. P( B |A)
c.
P(A|B)
d. P( A |B)
e. Given that an individual is selected at random and that he or she has at least one
card, what is the probability that he or she has a Visa card?
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III. If Charlie Brown pitches for his baseball team the probability that the team wins is 1/10.
However, if Charlie Brown does not pitch, then the probability of a win is ¾. Suppose Charlie
Brown pitches 1/3 of all games. Find:
(12 points)
1. The probability that Charlie Brown pitches and the team wins
2. The probability that Charlie Brown does not pitch and the team wins
3. The probability that the team wins
4. If the team wins, what is the probability that Charlie Brown was pitcher?
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IV. The lifespan in days of a certain carnivorous plant is a random variable X with probability
density function
1/20,000 0 < x < 200
f(x) =
0
othewise
20 points
1. What is the probability that this plant will live between 100 and 200 days?
2. What is the probability that the plant will live exactly 30 days?
3. What is the probability that the plant will die during the first 30 days?
4. Find the expected lifespan of the plant.
5. If some continuous random variable has density function
cx2 , 1 < x < 2
f(x) =
0
otherwise
Find the constant c.
5
V.
Suppose that only 25% of all drivers come to a complete stop at an intersection having
flashing red lights in all directions when no other cars are visible. What is the probability
that, of 20 randomly chosen drivers coming to an intersection under these conditions,
12 points
a. At most 6 will come to a complete stop?
b. Exactly 6 will come to a complete stop?
c.
At least 6 will come to a complete stop?
d. How many of the next 20 drivers do you expect to come to a complete stop?
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VI. Suppose the number X of tornadoes observed in Kansas during a 1-year period has a
Poisson distribution with   9.
8 points
a. Compute P( X  5).
b. Compute P(6  X  9).
c.
Compute P(10  X ).
d. How many tornadoes can be expected to be observed during the 10-year period?
What is the standard deviation of the number of observed tornadoes?
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VII. 8 points
1.The distribution of weights of a certain type of animal is known to be normal, with 10% of all
critters having a weight exceeding 12 pounds, and 5% having a weight less than 9 pounds.
What are the mean value and standard deviation of the weight distribution? Hint: you will need
the standard normal to solve this.
2. Use the normal distribution to answer the following question.
Suppose only 40% of all drivers in Florida regularly wear a seatbelt. A random sample
of 500 drivers is selected. What is the probability that Between 170 and 220 (inclusive)
of the drivers in the sample regularly wear a seatbelt?
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VIII. To pass the time, Joe Fafatone tosses a single die. He tosses the die 36 times and
calculates that the average value of his tosses is 4.0. He repeats the experiment and this time
gets an average value of 4.1. “Questo è vero?!?!” exclaims Joe in disbelief. Having studied
extensively at Foxwoods University, Joe knows that in theory when he tosses a single die the
expected value is 3.5 with standard deviation of 1.7.
Thirty-six tosses—twice—with an average over 4.0 both times? This seems incredible to Joe--but
maybe not.
Consider the following experiment:
Toss a single die 36 times and calculate the average of the thirty-six tosses.
If you perform the experiment twice, what is the probability that both averages are greater than
4.0?
5 points
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