## Transcribed Text

1. (15 Marks) The following are body mass index (BMI) scores measured in 11 patients
who
are free of diabetes and participating in a study of risk factors for obesity. Body
mass index is measured as the ratio of weight in kilograms to height in meters squared.
25, 27, 31, 28, 28, 41, 24, 32, 46, 35 and 40
Find the following:
a) Mean (1 point)
b) Median (1 point)
c) Range (1 point)
d) Lower Quartile (Q1) (1 point)
e) Upper Quartile (Q3) (1 point)
f) Interquartile Range (IQR) (1 point)
g) Lower Fence (1 point)
h) Upper Fence (1 point)
i) Construct a box-plot. Are there potential outliers in the data? Justify your answer.
(2 points)
j) Compute the sample standard deviation and sample variance. (3 points)
k) Which statistics would you use to identify the center and the spread of this distri-
bution? Explain. (2 points)
2. (8 Marks - 2 points each) Suppose you toss a fair coin four times. Let the random
variable X be the number of tails (T) obtained. Also, let E and V denote the mean
and variance respectively.
a) Compute E(X) and V(X).
b) Compute E(5X - 6) and V(6 + 5X).
3. (9 Marks) The length of time required by students to complete a one-hour exam is
a random variable with a probability density function (pdf) given by f(x) = c.x³ + x²,
0 < X < 1.
a) Find the value C and write down the new pdf. (2 points)
C
b) Find the probability that a randomly selected student will finish in less than half
an hour. (3 points)
c) Find the mean and standard deviation of the distribution. (4 points)
mean =
SD =
4.
(8
Marks)
Suppose
X
is
a
random
variable best described by a uniformly distribution
or probability that ranges from 2 to 11.
a) Write down the probability density function f(x). (1.5 points)
b) Compute the following:
i) mean (1.5 points)
ii) standard deviation (1.5 points)
iii) P(X < 3.858) (1.5 points)
iv) P(u - (2 points)
5. (5 Marks) At a certain gas station, 60% of the customers use Regular gas (A1), 20%
use Plus gas (A2), and 20% use Premium (A3). Of those customers using regular gas,
only 45% fill their tanks (event B). Of those customer using plus, 50% fill their tanks,
whereas of those using premium, 55% fill their tanks. If the next customer fills the
tank, what is the probability that Plus gas is requested?
6.
(5
Marks) A group of four undergraduate and five graduate students are available
to fill certain student government posts. If four students are to be randomly
selected
from this group,
a) Find the probability that exactly two undergraduates will be among the
four
chosen.
(2 points)
b) What is the probability that at least two graduate students be chosen? (3 points)

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