GENG 2220
HW#4
Name:_______________________________
Student #:_________________________________
1) Discrete random variables are obtained from data that can be measured rather than
counted.
A) True
B) False
2) Continuous variables have values that can be measured.
A) True
B) False
3) Determine whether the random variable described is discrete or continuous. The number of
minutes you must wait in line at the grocery store
A) continuous
B) discrete
4) Determine whether the random variable described is discrete or continuous. The total value of
a set of coins
A) discrete
B) continuous
5) Determine whether the random variable described is discrete or continuous. The number of 3point shots made in a basketball game
A) discrete
B) continuous
6) Determine whether the random variable described is discrete or continuous. The length in
seconds of a randomly-selected TV commercial
A) discrete
B) continuous
7) The sum of the probabilities of all the events in the sample space of a probability distribution
must equal 1.
A) True
B) False
8) A variable is one in which values are determined by chance.
A) discrete
B) sampled
C) continuous
D) random
9) A probability distribution consists of the finite number of values a random variable can
assume and the corresponding probabilities of the values.
A) sampled
B) discrete
C) continuous
D) random
GENG 2220
HW#4
Name:_______________________________
Student #:_________________________________
10) Fill in the missing value so that the following table represents a probability distribution.
x
P(x)
2
0.28
3
0.5
4
?
5
0.02
A) 0.24
B) 0.20
C) 0.25
D) 0.14
P(all) = 1
P(x=4) = 1-(P(x=2)+ P(x=3)+ P(x=5)) =1-0.28-0.5-0.02=0.20
11) The number of song requests a radio station receives per day is indicated in the table below.
Construct a graph for this data. (C)
Number of calls X
Probability P(X)
8
0.21
9
0.31
10
0.16
A)
B)
C)
D)
11
0.14
12
0.18
GENG 2220
HW#4
Name:_______________________________
Student #:_________________________________
12) The following table presents the probability distribution of the number of vacations X taken
last year for a randomly chosen family. Find the probability that a family took at least 3
vacations last year.
x
P(x)
0
0.13
1
0.58
2
0.15
3
0.1
4
0.04
A) 0.86
B) 0.14
C) 0.29
D) 0.1
P(x>=3) = P(x=3)+P(x=4) = 0.1+0.04 =0.14
13) A survey asked 895 people how many times per week they dine out at a restaurant. The
results are presented in the following table.
Number of Times
0
1
2
3
4
5
6
7
Total
Frequency
126
269
233
133
80
22
28
4
895
Consider the 895 people to be a population. Let X be the number of times per week a person
dines out for a person sampled at random from this population. Find the probability that a person
does not dine out at all.
A) 0.301
B) 0.441
C) 0
D) 0.141
P(x=0) = 126/895=0.141
14) The following table presents the probability distribution of the number of vacations X taken
last year for a randomly chosen family. Compute the mean µ.
x
P(x)
A) 1.29
0
0.09
B) 0.88
1
0.68
C) 1.38
2
0.12
D) 0.77
Mean = Σ[X ×P(X)] = 0*0.09+1*0.68+2*0.12+3*0.07+4*0.04=
3
0.07
4
0.04
GENG 2220
HW#4
Name:_______________________________
Student #:_________________________________
15) A researcher wishes to determine the number of cups of coffee a customer drinks with an
evening meal at a restaurant. Find the variance.
x
P(x)
A) 1.061
0
0.31
1
0.42
B) 1.062
C) 1.030
2
0.19
3
0.03
4
0.05
D) 1.09
𝜇𝜇 = Σ[𝑋𝑋 ×P(𝑋𝑋)] = 0 × .31 + 1 × .42 + 2 × .19 + 3 × .03 + 4 × .05 = 1.09
𝜎𝜎𝑋𝑋2 = Σ𝐸𝐸[(𝑋𝑋 − 𝜇𝜇)2 ] = Σ[𝑋𝑋 2 × 𝑃𝑃(𝑋𝑋)] − 𝜇𝜇 2 = [02 × 0.31 + ⋯ 42 × 0.05] − 1.092 = 1.0619
16) A person pays $1.00 to play a certain game by rolling a single die once. If a 1 or a 2 comes
up, the person wins nothing. If, however, the player rolls a 3, 4, 5, or 6, he or she wins the
difference between the number rolled and $1.00. Find the expectation for this game.
A) $2.00
B) $0
C) $1.00
D) $1.33
Expected result is winnings minus cost of playing:
$2.33 - $2 = $1.33
17) A coin is tossed five times. Find the probability of getting exactly three heads.
A) 0.800
B) 0.156
C) 0.125
D) 0.313
N=5, x=3, p=.5
From table, 0.312
Or
P(X=3)=5C3×0.53×(1−0.5)5−3=0.03125
18) A student takes a true-false test that has 13 questions and guesses randomly at each answer.
Let X be the number of questions answered correctly. Find P(Fewer than 4)
A) 0.0461
B) 0.8666
C) 0.0112
D) 0.1334
P(X<4)=P(X≤3)
=P(X=0)+P(X=1)+P(X=2)+P(X=3)=
13C0×0.50×(1−0.5)13−0+13C1×0.51×(1−0.5)13−1+13C2×0.52×(1−0.5)13−2+13C3×0.53×(1−0
.5)13−3=0.0461
Or from table, 0.002+0.010+0.035=0.047
GENG 2220
HW#4
Name:_______________________________
Student #:_________________________________
19) A computer store has 75 printers of which 40 are laser printers and 35 are ink jet printers. If a
group of 10 printers is chosen at random from the store, find the mean of the number of ink jet
printers.
A) 1.6
B) 4.7
C) 5.3
D) 2.5
35
= 0.467, 𝑛𝑛 = 10
75
𝐸𝐸(𝑥𝑥) = 𝑛𝑛𝑛𝑛 = 0.467 ∗ 10 = 4.7
𝑝𝑝 =
20) A certain large manufacturing facility produces 20,000 parts each week. The manager of the
facility estimates that about 1% of the parts they make are defective. What is the variance for the
number of defective parts made each week?
A) 14.1
B) 198
C) 138
D) 200
𝜎𝜎 2 = 𝑛𝑛𝑛𝑛(1 − 𝑝𝑝) = 20000 ∗ 0.1 ∗ 0.99 = 198