MAT150-LS17 Midterm Review

This is a review guide for the MAT150-LS17 Midterm exam. It covers topics such as qualitative and quantitative data, probability distributions, and more. The instructor for this course is Frederic Anglade. The guide includes sample questions and answers to help you prepare for the exam.

BOROUGH OF MANHATTAN COMMUNITY COLLEGE
MAT150-LS17
Midterm Review
Instructor: Frederic Anglade
1) Determine whether the data are qualitative or quantitative.
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1a) the colors of automobiles on a used car lot
A) Qualitative
1b) the number of complaint letters received by the United States Postal Service in a given day
B) Quantitative
1c) the number of seats in a movie theater
A) Quantitative
1d) the numbers on the shirts of a girl's soccer team
A) Qualitative
Determine whether the data set is a population or a sample.
1e) the age of every fourth person entering a department store
B) Sample
1f) the age of each employee at a local grocery store
B) Population
2) Identify the population and the sample.
2a) Population: American households; Sample: American households who own a computer.
2b) Population: American households; Sample: American households who owned two cars.
2c) Population: Elementary school children; Sample: Elementary school children who could be
classified as obese.
2d) A) Population: Magazine subscribers; Sample; Magazine subscribers who renew their
subscription
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3) Identify whether the statement describes inferential statistics or descriptive statistics.
3a) the average age of the students in a statistics class is 20 years.
B) Descriptive statistics
3b) the chances of winning the California Lottery are one chance in twenty-two million.
B) Descriptive statistics
3c) there is a relationship between smoking cigarettes and getting emphysema.
B) Inferential statistics
3d) from past figures, it is predicted that 31% of the registered voters in California will vote in the
June primary.
B) Descriptive statistics
3e) based on previous clients, a marriage counselor concludes that the majority of marriages that
begin with cohabitation before marriage will result in divorce.
A) Inferential statistics
4) Use the given frequency distribution to find the
(a) Class width.
(b) Class midpoints of the first class.
(c) Class boundaries of the first class.
4a) Height (in inches)
D) (a) 3 (b) 51 (c) 49.5-52.5
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4b) Phone Calls (per day)
B) (a) 4 (b) 9.5 (c) 7.5-11.5
6a) The heights (in inches) of 30 adult males are listed below
a) Construct a frequency distribution, a relative frequency distribution, and a cumulative frequency
distribution using five classes.
CLASS LL UL MID FREQUENCY REL.FREQ CUM.FREQ
67-68.5 67 68.5 67.75 6 0.20 6.00
68.5-70 68.5 70 69.25 10 0.33 16.00
70-71.5 70 71.5 70.75 8 0.27 24.00
71.5-73 71.5 73 72.25 4 0.13 28.00
73-74.5 73 74.5 73.75 2 0.07 30.00
b) Construct a frequency histogram using five classes.
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c) Construct a relative frequency histogram using five classes.
d) Construct a frequency polygon using five classes.
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e) Construct an Ogive using five classes.
For the given data, construct a frequency distribution and frequency histogram of the data using five
classes. Describe the shape of the histogram as symmetric, uniform, skewed left, or skewed right.
7a) Data set: California Pick Three Lottery
C) Uniform
CLASS LL UL MID FREQUENCY REL.FREQ CUM.FREQ
0-1.8 0 1.8 0.9 6 0.20 6.00
1.8-3.6 1.8 3.6 2.7 6 0.20 12.00
3.6-5.4 3.6 5.4 4.5 6 0.20 18.00
5.4-7.2 5.4 7.2 6.3 6 0.20 24.00
7.2-9 7.2 9 8.1 6 0.20 30.00
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8b) The test scores of 30 students are listed below. Find the five-number summary
D) Min = 31, Q1 = 58, Q2 = 72, Q3 = 83, Max = 99
ANS: Arranging the data in ascending order we get
31 41 45 48 52 55 56 58 63 65
67 67 69 70 70 74 75 78 79 79
80 81 83 85 85 87 90 92 95 99
Q1=( n+1
4 ) th
Observation = 7.75th observation = 56 + 0.75 * (58 – 56) = 57.5
Q2=( n+1
2 )
th
Observation = 15.5th observation = 70 + 0.5 * (74 – 70) = 72
Q3=3∗( n+1
4 )
th
Observation = 23.25th observation = 83 + 0.25 * (85 – 83) = 83.5
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9a) Find the z-score for the value 79, when the mean is 55 and the standard deviation is 5.
B) z = 4.80
ANS: Mean = μ = 55 and the standard deviation = σ = 5
Here, X = 79 and
Z = X−μ
σ =79−55
5 =4 . 8
10a) The graph below is an Ogive of scores on a math test
Percentile Ranks of Math Test Scores
Use the graph to approximate the percentile rank of an individual whose test score is 60.
B) 37
ANS: Percentile rank of an individual denotes the percentage of students equal or below to that
student. From the Ogive it is identified that the test score is 60 intersects under the percentile score
of 40. Hence, percentile rank = 37 is the probable answer.
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11a) A single six-sided die is rolled. Find the probability of rolling a number less than 3.
A) 0.333
ANS: Let X denote the face value of a dice. Then, required probability =
P ( X <3 ) =P ( X =1 ) + P ( X=2 ) =1
6 + 1
6 = 1
3 =0 . 333
12a) The distribution of Master's degrees conferred by a university is listed in the table.
What is the probability that a randomly selected student graduating with a Master's degree has a
major of Engineering? Round your answer to three decimal places
C) 0.099
ANS: Total number of graduating with a Master's degree = (216 + 207 + 90 + 176 + 222) = 911
Favorable number of students graduating with a Master's degree has a major of Engineering = 90.
Hence, required probability =
favorable cases
total cases =90
911 =0 . 099
13a) Classify the events as dependent or independent. Events A and B where
P (A) = 0.5, P (B) = 0.1, and P (A and B) = 0.05
B) Independent
ANS: As, P ( A∩B ) =0. 05=P ( A )∗P ( B ) , events A and B are independent.
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14a) A group of students were asked if they carry a credit card. The responses are listed in the table.
If a student is selected at random, find the probability that he or she owns a credit card given that
the student is a sophomore. Round your answer to three decimal places
B) 0.975
ANS: From the above provided table we get that total number of respondents are = N = 100
Now, let A = student is a sophomore, and B = student owns a credit card
Required conditional probability =
P ( B / A ) = P ( B∩ A )
P ( A ) =39/ 100
40/ 100 =39
40 =0 . 975
15b) Given that P (A or B) = 1
2 , P (A) = 1
3 , and P (A and B) = 1
9 , find P (B)
C) 5
18
ANS:
P ( A∪B ) = 1
2 , P ( A ) = 1
3 , P ( A∩B ) = 1
9
Now, P ( A∪B ) =P ( A ) + P ( B ) −P ( A∩B )
=> 1
2 =1
3 + P ( B ) − 1
9
=> P ( B ) = 1
2 −1
3 + 1
9 = 5
18
16a)
B) 90
ANS:
10 P2=10 !
( 10−2 ) ! =10∗9=90
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17b) A tourist in Ireland wants to visit six different cities. How many different routes are possible?
D) 720
ANS: There are 6 ! different possible routes for the tourist to visit six different cities. The visitor can
visit the cities in 6! = 720 different possible orders or ways.
18a) Determine the probability distribution's missing value.
The probability that a tutor will see 0, 1, 2, 3, or 4 students
D) 1
21
ANS: Total Probability = 1
Hence, total probability for the above probability distribution is
2
21 + 1
3 + 2
21 +? + 3
7 =1
Therefore, the missing probability
=1− 2
21 − 1
3 − 2
21 − 3
7 = 1
21
19a) The random variable x represents the number of boys in a family of three children. Assuming
that boys and girls are equally likely, find the mean and standard deviation for the random variable x
D) Mean: 1.50; standard deviation: 0.87
ANS: The probability distribution of number of boys in a family is as follows, where X denotes the
number of boys in a family.
X 0 1 2 3
P(X) a b c d
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The probabilities are calculated as follows.
a=3 C0 ( 1
2 )
3
=1
8
b=3C1 ( 1
2 ) 3
= 3
8
c=3 C2 ( 1
2 )
3
= 3
8
d=3 C3 ( 1
2 )
3
= 1
8
So, Mean =
E ( X ) =0∗a+1∗b +2∗c+3∗d=0∗1
8 +1∗3
8 +2∗3
8 +3∗1
8 =3
2 =1 .5
Again,
E ( X2 ) =02∗a+12∗b+22∗c+32∗d=0∗1
8 +12∗3
8 + 22∗3
8 +32∗1
8 =24
8 =3
Var ( X ) =E ( X2 ) − { E ( X ) }
2=3−1. 52=3−2 . 25=0 . 75
SD= √ Var ( X ) = √ 0 .75=0 . 866=0. 87
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