Math 3
Review (3B and 3.12)
Name:
Date:
1. Calculate the mean, variance, and standard deviation for the data set. Show your work
(you may wish to add columns to this table)
x Frequency 0 2 1 2 3 4 5 3 7 1 8 2 10 2 2. A certain data set has the following statistics:
σ 2 = 20
x=3
σ = 4.472
a. Find the mean, variance and standard deviation if you add 6 to each number in the
data set.
x=
σ2 =
σ=
b. Find the mean, variance and standard deviation if you multiply each number in
the data set by 2.
x=
σ2 =
σ=
3. Consider two number cubes with different numbers on their faces:
Cube 1: 2, 3, 3, 5, 6, 8
Cube 2: 2, 4, 5, 6, 7, 9
Find the mean, variance, and standard deviation of the sum when rolling the two
number cubes.
4. Recall the statistics for a regular number cube:
σ 2 = 2.917
x = 3.5
σ = 1.708
a. Find the mean, variance, and standard deviation for the sum of 20 number cubes.
b. Find the mean, variance, and standard deviation for the sum of 100 number
cubes.
5. What is the probability of getting 10 questions correct on a 30 questions multiplechoice test where each question has 4 options?
6. At a certain high school, 35% of the students participate in music.
a. Find the mean, variance, and standard deviation for the number of students who
will say they participate in music if you ask 100 students.
b. Suppose you ask 100 students and 38 say they participate in music. Calculate the
z-score for your result.
c.
Is your result unusual or typical?
7. Recall the statistics for a multiple-choice question with 5 options:
σ 2 = 0.16
x = 0.2
σ = 0.4
a. Find the mean, variance, and standard deviation for the number of questions
correct on a 25-question test.
b. Find the mean, variance, and standard deviation for the number of questions
correct on a 50-question test.
8. What is the probability of getting 5 odd numbers if you roll 10 number cubes?
9. Find the mean, variance, and standard deviation for the number of snowy days in the
next week if there is a 40% chance of snow each day.
10. A campaign manager thinks 45% of voters prefer his candidate. Find the mean,
variance, and standard deviation for the number of voters who will say they prefer
this candidate if you ask 500 voters.
Answers
72
1. x = 16
= 4.5
σ 2 = 166
16 = 10.375
σ = 10.375 = 3.221
2. a. x = 3+ 6 = 9 σ = 20
σ = 4.472
2
2
b. x = 3⋅ 2 = 6
σ = 20 ⋅ 2 = 80
σ = 4.472 ⋅ 2 = 8.944
3. Cube 1: x = 4.5 σ = 2.062
Cube 2: x = 5.5 σ = 2.217
2
Sum: x = 4.5 + 5.5 = 10 σ = 2.062 2 + 2.2172 = 9.167
σ = 9.167 = 3.028
2
4. a. x = 3.5⋅ 20 = 70
σ = 2.917 ⋅ 20 = 58.34
σ = 58.34 = 7.638
2
b. x = 3.5⋅100 = 350
σ = 2.917 ⋅100 = 291.7
σ = 291.7 = 17.079
! 30 $
&⋅ (0.25)10 ⋅ (1− 0.25)30−10 = 0.091
5. #
10
"
%
2
2
6. a. x = 100(0.35) = 35 σ = 100(0.35)(1− 0.35) = 22.75 σ = 22.75 = 4.770
b. 0.629
c. The result is typical. It is within 1 standard deviation of the mean.
7. a. x = 0.2 ⋅ 25 = 5
σ 2 = 0.16 ⋅ 25 = 4
σ = 4 =2
2
b. x = 0.2 ⋅ 50 = 10
σ = 0.16 ⋅ 50 = 8
σ = 8 = 2.828
! 10 $
&⋅ (0.5)5 ⋅ (1− 0.5)10−5 = 0.246
8. #
" 5 %
2
σ = 1.68 = 1.296
9. x = 7(0.4) = 2.8 σ = 7(0.4)(1− 0.4) = 1.68
2
σ = 123.75 = 11.124
10. x = 500(0.45) = 225 σ = 500(0.45)(1− 0.45) = 123.75