AMS 310, Test 1
Part 1 Circle the best answer Solutions indicated in red
1. The following are octane levels for various gasoline blends:
87.8, 84.9 86.7 87.5 91.6 88.6 95.1 93.3 94.2 88.3 90.4 91.5 91.6 93.4
Which of the following stem-and-leaf plots describe the distribution more efficiently?
a) a stem-and-leaf plot by using the tens digit as the stem
b) a stem-and-leaf plot by using the first two digits (tens and ones digits) as the stem
c) Neither of these
2. In a study of a parasite in animals, researchers measured the lengths (in μm) of 100 individual
parasites of certain species from the blood of a mouse. The measures are shown in the
following table. Compute the mean (write it up to the second decimal place).
Length 20 21 22 23 24 25 26 27 28 29 30
Frequency 3 2 12 10 15 16 14 13 11 3 1
a) 24.00 b) 25.00 c) 25.96 d) 24.96 e) None of these
3. For two events A and B, the probability that A occurs is 0.8, the probability that B occurs is
0.4, and the probability that both occurs is 0.2. Given that A occurred, what is the probability
that B also occurred (write up to second decimal place)?
a) 0.35 b) 0.30 c) 0.20 d) 0.25 e) 0.40 f) None of these
4. If a student is randomly choosing the answer to each of ten true-false questions in a test,
what is the probability that he will have at most one incorrect answer (express the answer with
four decimal places)?
a) 0.0010 b) 0.0107 c) 0.0009 d) None of these
5. Let X be a random variable with cdf
Find P(1.5 < X ≤ 3) (express the answer with two decimal places).
a) 0.55 b) 0.60 c) 0.50 d) 0.45 e) 0.60 f) None of these
, Part 2 Show all work do not just give answers
1. The following are the amounts of radiation received at a greenhouse.
6.4 7.2 8.5 8.9 9.1 10.0 10.1 10.2 10.6 10.8 11.0 11.2 11.3 11.4 12.0 12.3 13.2
a) Find the median and the quartiles Q1 and Q3. Show your reasoning.
Median = x n+1 =x 17+1 =x(9)=10.6
( ) ( )
2 2
Q1=( 17)(.25)=4.25 ↑5 → x(5)=9.1
Q3=(17)(.75)=12.75↑ 13 →x(13)=11.3
b) Create a box plot for this data. Include a scale and label the key 5 numbers.
Q1 = median= Q3 =
min= 9.1 10.6 11.3 max=
6.4 13.2
2. The following are midterm scores of an algebra class of 20 students in a high school:
69 84 52 93 81 74 89 85 88 63 87 64 67 72 74 55 82 91 68 77
a) Find the inter quartile range.
Q1=( 20)(.25)=5→ x(5)=67
Q3=(20)(.75)=15→ x(15)=85
IQR = Q3 – Q1
IQR = 85 – 67 = 18
b) Find the cutoff points for outliers, and determine if there are any outliers.
Lower cutoff = Q1 – 1.5(IQR)
Lower cutoff = 67 – 1.5(18) = 40 -> no lower outliers
Upper cutoff = Q3 + 1.5(IQR)
Upper cutoff = 85 + 1.5(18) = 112 -> no upper outliers
Part 1 Circle the best answer Solutions indicated in red
1. The following are octane levels for various gasoline blends:
87.8, 84.9 86.7 87.5 91.6 88.6 95.1 93.3 94.2 88.3 90.4 91.5 91.6 93.4
Which of the following stem-and-leaf plots describe the distribution more efficiently?
a) a stem-and-leaf plot by using the tens digit as the stem
b) a stem-and-leaf plot by using the first two digits (tens and ones digits) as the stem
c) Neither of these
2. In a study of a parasite in animals, researchers measured the lengths (in μm) of 100 individual
parasites of certain species from the blood of a mouse. The measures are shown in the
following table. Compute the mean (write it up to the second decimal place).
Length 20 21 22 23 24 25 26 27 28 29 30
Frequency 3 2 12 10 15 16 14 13 11 3 1
a) 24.00 b) 25.00 c) 25.96 d) 24.96 e) None of these
3. For two events A and B, the probability that A occurs is 0.8, the probability that B occurs is
0.4, and the probability that both occurs is 0.2. Given that A occurred, what is the probability
that B also occurred (write up to second decimal place)?
a) 0.35 b) 0.30 c) 0.20 d) 0.25 e) 0.40 f) None of these
4. If a student is randomly choosing the answer to each of ten true-false questions in a test,
what is the probability that he will have at most one incorrect answer (express the answer with
four decimal places)?
a) 0.0010 b) 0.0107 c) 0.0009 d) None of these
5. Let X be a random variable with cdf
Find P(1.5 < X ≤ 3) (express the answer with two decimal places).
a) 0.55 b) 0.60 c) 0.50 d) 0.45 e) 0.60 f) None of these
, Part 2 Show all work do not just give answers
1. The following are the amounts of radiation received at a greenhouse.
6.4 7.2 8.5 8.9 9.1 10.0 10.1 10.2 10.6 10.8 11.0 11.2 11.3 11.4 12.0 12.3 13.2
a) Find the median and the quartiles Q1 and Q3. Show your reasoning.
Median = x n+1 =x 17+1 =x(9)=10.6
( ) ( )
2 2
Q1=( 17)(.25)=4.25 ↑5 → x(5)=9.1
Q3=(17)(.75)=12.75↑ 13 →x(13)=11.3
b) Create a box plot for this data. Include a scale and label the key 5 numbers.
Q1 = median= Q3 =
min= 9.1 10.6 11.3 max=
6.4 13.2
2. The following are midterm scores of an algebra class of 20 students in a high school:
69 84 52 93 81 74 89 85 88 63 87 64 67 72 74 55 82 91 68 77
a) Find the inter quartile range.
Q1=( 20)(.25)=5→ x(5)=67
Q3=(20)(.75)=15→ x(15)=85
IQR = Q3 – Q1
IQR = 85 – 67 = 18
b) Find the cutoff points for outliers, and determine if there are any outliers.
Lower cutoff = Q1 – 1.5(IQR)
Lower cutoff = 67 – 1.5(18) = 40 -> no lower outliers
Upper cutoff = Q3 + 1.5(IQR)
Upper cutoff = 85 + 1.5(18) = 112 -> no upper outliers
