Download Prob and Stats Practice Test Group 2 Prob and Stats

Jenny Park, Shina Cook, Alexis Martin, Liz Hood
IB MATH SL
Chapters 3, 8, 15 TEST
110 Points
Name ____________________________
3.1-3.4 Theoretical, Subjective, and Conditional Probability
1. Each letter of the word GIRAFFE is written on a separate card. The 7 cards are placed
downwards. A card is drawn at random. What is the probability of picking a card with:
a. The letter “F”
b. A consonant
Solution:
a. 2/7
b. 4/7
2. In a class of 25 students, 15 of them study French, 13 study Spanish, and 5 study neither.
If one student is chosen at random from the class, what is the probability that he studies
both French and Spanish?
Solution:
15=F
13=S
7
8
5
5


25-5=20
7+8=15
8+5=13
Therefore 8 studies both French and Spanish
3. Three unbiased coins are tossed one at a time, and the results are noted. One possible
outcome is that all the coins are heads. This is written HHH. Another is that the first 2
coins are heads and the last is a tail. It is written HHT. Find the probability that:
a. The number of heads is greater than the number of tails
b. Heads and tails are tossed alternatively
Jenny Park, Shina Cook, Alexis Martin, Liz Hood
Solution:
H
H
T
H
T
T
H
T
H
T
H
T
H
T
a. 4/8=1/2
b. 2/8=1/4
4. A teacher gave her class an IB Paper 1 and IB Paper 2. 35% of the class passed both tests
and 52% passed the first. What percentage of those who passed the first test also passed
the second test?
Solution:
. 35
= .673 = 67.3%
. 52
8.5 Cumulative Frequency
5. Fifty batteries were tested to see how long they lasted. The results are shown in the table.
Draw a frequency diagram and find the median and interquartile range
Time (h)
0≤ℎ<5
5 ≤ ℎ < 10
10 ≤ ℎ < 15
15 ≤ ℎ < 20
20 ≤ ℎ < 25
25 ≤ ℎ < 30
30 ≤ ℎ < 35
Solution:
Frequency (f)
3
5
8
10
12
7
5
Jenny Park, Shina Cook, Alexis Martin, Liz Hood

Add a cumulative frequency column to the table
Time (h)
Frequency (f)
0≤ℎ<5
5 ≤ ℎ < 10
10 ≤ ℎ < 15
15 ≤ ℎ < 20
20 ≤ ℎ < 25
25 ≤ ℎ < 30
30 ≤ ℎ < 35

Cumulative Frequency
3
5
8
10
12
7
5
3
8
16
26
38
45
50
Draw a graph to find interquartile range and median
Cumulative Frequency
60
50
40
30
Cumulative Frequency
20
10
0
5
10
15
20
25
30

Median of Range:
50/2=25
Estimate the x-value by using the graph
Median is approximately 19.

IQR= 3rd quartile – 1st quartile
50/.25=12.5
o Estimated x-value is approximately 13
50/.75=37.5
o Estimated x-value is approximately 25
IQR=25-19
IQR=12
8.6 Variance and Standard Deviation
35
Jenny Park, Shina Cook, Alexis Martin, Liz Hood
6. Calculate the mean and standard deviation by hand:
Thirty farmers were asked how many workers they hire for the harvest season.
Their responses were:
4, 5, 6, 5, 3, 2, 8, 0, 4, 6, 7, 8, 4, 5, 7, 9, 8, 6, 7, 5, 5, 4, 2, 1, 9, 3, 3, 4, 6, 4
Solution:
-5
-4
-3
-2
-1
0
1
2
3
4
𝜇=

(𝑥 − 𝜇)2
(𝑥 − 𝜇)
Workers (x)
Frequency (f)
𝑓∗𝑥
0
1
0
1
1
1
2
2
4
3
3
9
4
6
24
5
5
25
6
4
24
7
3
21
8
3
24
9
2
18
Total:
30
150
 Calculate Mean:
25
16
9
4
1
0
1
4
9
16
𝑓(𝑥 − 𝜇)2
25
16
18
12
6
0
4
12
27
32
152
150
=5
30
Calculate Standard Deviation:
152
𝜎=√
= 2.25
30
15.1 Random Variables
7. A fair six-sided dice has a “1” on one face, a “2” on two of its faces and a “3” on the
remaining three faces. The dice is thrown twice. T is the random variable “the total score
thrown”. Find
a. The probability distribution of T.
b. The probability that the total score is more than 4.
Solution:
Make a table of all outcomes
1
2
1
2
3
2
3
4
2
3
4
3
4
5
3
4
5
3
4
5
2
3
4
4
5
5
5
3
4
5
5
6
6
6
3
4
5
5
6
6
6
3
4
5
5
6
6
6
Jenny Park, Shina Cook, Alexis Martin, Liz Hood
a. Probability Distribution of T
X
2
3
P(X=x)
1/36
1/9
4
5/18
5
1/3
6
1/4
b. P(T>4)= 1/3 + 1/4 = 7/12
15.2 Binomial Distribution
8. In an examination hall, it is known that 15% of the desks are wobbly.
a. What is the probability that, in a row of six desks, more than one will be wobbly?
b. What is the probability that exactly one will be wobbly in a row of six desks?
Solution:
9. X is a random variable such that 𝑋~𝐵(𝑛, 𝑝). Given that the mean of the distribution is
7.8, and p=0.3 find:
a. n
b. The variance of X
Solution:
15.3 Normal Distribution
10. Given that Z ~ N (0,1), use your calculator to find
a. 𝑃 (0.2 < 𝑋 < 1.2)
b. 𝑃 (−2 < 𝑋 ≤ 0.3)
Solution:
Jenny Park, Shina Cook, Alexis Martin, Liz Hood
11. The random variable X~N(48, 81) Find:
a. P(X<52)
b. P(37<X<47)
Solution: