Exam Questions:
1) X is binomially distributed with 4 trials and a probability of success equal to ½ on
each trial. Calculate the probability of:
a.
b.
c.
d.
P(X=1)
P(X < 1)
P(X ≤ 1)
P(X ≥ 1)
a. 1/4
b. 1/16
c. 5/16
d. 15/16
2) If X~B(6, 1/3) find to 3 significant figures:
a. P(X = 2)
b. P(X < 2)
c. P(X ≤ 2)
d. P(X ≥ 2)
a. 0.329
b. 0.351
c. 0.680
d. 0.649
3) If X is binomially distributed with 8 trials and a probability of success equal to 2/7 at
each attempt, what is the probability of:
a. Exactly 5 successes
b. Less that 5 success
c. More than 5 successes
d. At least one success
a. 0.0389
b. 0.952
c. 0.00870
d. 0.932
4) These are the test scores for Mr. Wahbeh's class: 76, 79, 76, 74, 75, 71, 85, 82, 82, 79,
81 Use these to find:
a. The range
b. The median
c. The lower quartile
d. The upper quartile
e. The interquartile range
a. 14
b. 79
c. 75
d. 82
e. 7
5) Use the chart to create a graph and find (a) the median (b) the interquartile
range:
Time (min)
Number of
Students
2 and under
0
4 and under
6
6 and under
18
8 and under
24
10 and under
40
12 and under
60
14 and under
78
16 and under
92
18 and under
100
a. about 11
b. about 5.5
6) Find the Variance and standard deviation of:
a. 27, 44, 32, 49
b. 35, 65, 84, 27, 66
a. Variance = 78.5, Standard Deviation = 8.86
b. Variance = 449, Standard Deviation = 21.3
7) The number of children in the families in a class of 29 children is given in the table
below. Use this data to find (a) the mean and (b) the standard deviation:
Children
1
2
3
4
5
6
7
Frequency
5
12
8
3
0
0
1
a. Mean = 2.5
b. Standard Deviation = 1.24
8) X is binomially distributed with 7 trials with a probability of success that is 1/3
Determine the probability of
A). P(X = 2)
B). P(X = 1)
B). P(X > 3)
C). P(X ≤ 3)
A). 30.7%
B). 20.48%
C).17.33%
9) Find the area underneath a standard normal curve
A). Between 2 and 3 standard deviations from the mean
D). 82.67%
B). Between -2.5 and 2 Standard deviations from the mean
A). 2.14%
B). 97.1%
10) The Random Variable X has the probability distribution
Z
P(Z=z)
2
1/6
3
1/6
5
1/6
7
t
11
y
And E(Z) = 5 2/3
Find t and y
t = 3/8
y = 1/8
11) Phinn flips a coin 8 times what is the probability that he achieves heads every single
time.
1/256
12) 48% of all teenagers own a skateboard and 39% of all teenagers own a skateboard and
roller blades. What is the probability that a teenager owns roller blades given that the
teenager owns a skateboard?
0.8125
13) Given that P(E’) = P(F) = 0.6 and P(E and F) = 0.24
a.
b.
c.
d.
Write down P(E)
Explain why E and F are independent
Explain why E and F are not mutually exclusive
Find P(E U F’)
a. 0.4
b. P(E) x P(F)= P(E & F)
c. P(E & F) ≠ 0
d. 0.64