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Probability and Statistics
Name______________________________
3rd 9 Weeks Exam Review (WITH PROBABILITY): Day 1
Directions:
1.
a.
b.
Directions:
2.
Probability Distributions. Determine the missing probability.
x
P(x)
3
0.398
6
?
9
0.166
12
0.410
x
P(x)
1
1/17
2
5/17
3
3/17
4
?
Probability Distributions. Find the mean, variance, and standard
deviation of the following.
a.
x
P(x)
0
0.12
1
0.2
2
0.31
3
0.25
4
0.12
Mean = ______________
Variance = ____________
St. Dev = _____________
b.
x
P(x)
8
0.15
9
0.25
10
0.29
11
0.19
12
0.12
Mean = ______________
Variance = ____________
St. Dev = _____________
c.
x
P(x)
0
0.17
1
0.26
2
0.13
3
0.24
4
0.20
Mean = ______________
Variance = ____________
St. Dev = _____________
Directions:
3.
Binomial Distributions. Answer the following.
The probability that a woman will color her hair is 0.72. What is the probability
that in a randomly selected group of 25 women,
a.
exactly 15 will color their hair?
b. at least 20 will color their hair?
c.
4.
at most 10 will color their hair?
The probability that a person has fallen asleep while talking on the phone is 0.34.
What is the probability that in a randomly selected group of 20 people,
a.
exactly 7 have fallen asleep while talking on the phone?
b. at least 13 have fallen asleep while talking on the phone?
c.
5.
at most 8 have fallen asleep while talking on the phone?
Approximately 75% of students have tried driving without a license. What is the
probability that in a randomly selected group of 40 people,
a.
exactly 30 students have driven without a license?
b. at least 28 students have driven without a license?
c.
6.
at most 31 students have driven without a license?
Approximately 72% of toddlers are willing to try peas. In a group of 45 toddlers,
what is the
a.
mean number of toddlers willing to try peas?
b. standard deviation?
7.
Approximately 33% of teachers have more than one college degree. In a school with
120 teachers, what is the
a.
mean number of teachers who have more than one degree?
b. the standard deviation?
Directions: Standard Normal Distributions. Find the following.
8.
What is the mean and standard deviation of a standard normal curve?
9.
State the empirical rule.
a.
b.
c.
10.
Percentage within 1 standard deviation about the mean: __________
Percentage within 2 standard deviations about the mean: __________
Percentage within 3 standard deviations about the mean: __________
a.
P(0  z  2.35)
b.
P(2.10  z  2.34)
c.
P ( z  0.13)
d.
P( z  1.48)
Directions:
Normal Applications. Find the following.
11.
Pizza delivery time is normally distributed. Pizzas are delivered in 30 minutes on
average with a standard deviation of 5.9 minutes. What is the probability it will
take more than 40 minutes for your pizza to be delivered?
12.
Assume that women’s heights are normally distributed with a mean of
  64.5 inches and a standard deviation given by   2.2 inches.
a.
If a woman is randomly selected, find the probability that her height is less
than 65 inches.
b. What height would a woman be if she was in the top 10% of the population?
13.
The average cholesterol content of a certain brand of eggs is 216 mg with a
standard deviation of 15 mg. Assume the variable is normally distributed. If an egg
is selected, find the probability that the cholesterol content will be between 210 mg
and 220 mg.
Directions:
Find the following probabilities.
14.
If the probability of NOT owning a cell phone is 0.12, what is the probability that a
person does own a cell phone?
12.
A card is drawn from a standard deck of cards. What is the probability it is a
diamond?
13.
A jar contains 3 red, 2 black, 6 purple, and 3 yellow balls. What is the probability of
randomly drawing a purple ball?
14.
Students were asked if they watched college football. The results are in the chart
below.
Watch College
Does NOT watch
Football
college football
9th graders
th
12 graders
32
84
73
43
If a student is selected at random, what is the probability that he or she will be a
9th grader or watch college football?
15.
In a survey of high school students, 326 students said they have texted during class
and 98 said they had not. From this, we can calculate the probability that a student
will text during class. Is this a theoretical or experimental (empirical) probability?
16.
The probability of getting 3 of a kind in poker is about 2.11%. Is this a theoretical
or experimental (empirical) probability?
17.
A group of high school students were asked if he or she had a video game system.
The results are listed below.
Owns a gaming system
male
female
258
157
Does NOT own a gaming
system
81
103
If a student is selected at random, what is the probability that the student will own
a video game system, given that the student is female?
Directions: Answer the following.
18.
Which measure determines the expected value of the variable?
19.
Use the table to answer the following questions.
x
P(x)
1
0.27
2
0.34
3
0.16
4
0.09
5
x
a. Find the missing value.
b. Find the expected value.
c. Find P ( x  4).
d. Find
Px  2.
20.
A school group is selling $3 raffle tickets. The first prize is $4,500 and the second
prize is $1,000. There are 10 prizes of $20 gift certificates. The number of
tickets sold is 4500. You purchase 1 ticket. Find the expected value of the gain.
21.
A cash prize of $3500 is to be awarded in a raffle. If 1800 tickets are sold at $5
each, find the expected value of the gain if you purchase 2 tickets.
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