Transcript Jepoardy review

Discrete
RV
Continuous
RV
Linear
Transform
ations
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Combinatio
ns 1
Combinatio
ns 2
The
Garcia’s
The median of a random variable is defined
as any value x such that P(X < x) > 0.5 and
P(X > x) > 0.5. For the probability
distribution shown in the table below,
determine the median of X.
x
0
1
2
3
4
5
p( x) 0.20 0.10 0.15 0.15 0.15 0.25
A 100
3
A 100
Player A rolls a six-sided die with 7 on four
sides and 11 on two sides (event A). Player B
flips a coin with 6 on one side and 10 on the
other (event B). Let X represent the sum of
the two events, what is the expected value of
X?
A 200
16.333
A 200
You pay $3 to play this game: You draw a
card from a standard 52 card deck. If you
get a red card, you win nothing. If you get a
spade, you win $5. For any club, you win
$10 plus an extra $20 for the ace of clubs.
What are your expected total winnings (net
profit)?
A 300
$1.13
A 300
You play two games against the same
opponent. The probability that you win the
first game is 0.4. If you win the first game,
the probability you also win the second is
0.2. If you lose the first game, the
probability that you win the second is 0.3.
Let X be the number of games you win,
what is the standard deviation of X?
A 400
0.62
A 400
Your company bids for two contracts. You
believe the probability you get contract #1 is
0.8. If you get contract #1, the probability that
you also get contract #2 will be 0.2, and if you
do not get contract #1, the probability that you
get contract #2 will be 0.3. Let X be the
number of contracts you get, what is the
standard deviation of X?
A 500
0.5474
A 500
Let the random variable X be a random
number with the density curve given
below. What is P(X = 0.5)?
B 100
0
B 100
Let the random variable X be a random
number with the density curve given
below. What is P(0.2 < x < 0.4)?
B 200
0.14
B 200
Let the random variable X be a random number with
the uniform density curve given below.
Find P(0.7 ≤ X ≤ 1.1):
B 300
0.3
B 300
The weight of medium-size tomatoes selected at
random from a bin at HEB is a normal random
variable with mean  = 10 ounces and standard
deviation  = 1 ounce.
The weight of the tomatoes in pounds (1 pound = 16
ounces) is a random variable with standard deviation
B 400
1/16
B 400
A continuous random variable X
has a probability density function
f(x) as shown below. Find the
value of “k”
B 500
1/3
B 500
Given independent random variables with
means and standard deviations as shown
Mean
St. Dev
X
10
2
Y
20
5
find the mean and standard deviation of 3X
C 100
30, 6
C 100
Given independent random variables with
means and standard deviations as shown
Mean
St. Dev
X
10
2
Y
20
5
find the mean and standard deviation of Y+ 6
C 200
26, 5
C 200
Given SAT = 40(ACT) +150 find:
The mean SAT score if the mean ACT score is 29
C 300
1310
C 300
A bicycle shop will be offering 2 specially
priced children’s models at a sidewalk sale. The
basic model will sell for $120 and the deluxe
model for $150. Past experience indicates that
sales of the basic model will have a mean of 5.4
bikes with a standard deviation of 1.2, and sales
of the deluxe model will have a mean of 3.2
bikes with a standard deviation of 0.8. The cost
of setting up for the sidewalk sale is $200.
What is the mean of the net income?
C 400
$928
C 400
A bicycle shop will be offering 2 specially priced
children’s models at a sidewalk sale. The basic
model will sell for $120 and the deluxe model for
$150. Past experience indicates that sales of the
basic model will have a mean of 5.4 bikes with a
standard deviation of 1.2, and sales of the deluxe
model will have a mean of 3.2 bikes with a
standard deviation of 0.8. The cost of setting up for
the sidewalk sale is $200.
What is the standard deviation of the net income?
C 500
$187.45
C 500
Consider a small ferry that can accommodate cars
and buses. The toll for cars is $3 and the toll for
buses is $10. Let x and y denote the number of
cars and buses, respectively, carried on a single
trip. Suppose that x = 2.8 and 2x = 1.66 and that
y = .7 and 2y = .61. Assume all events are
independent.
Let z= total number of vehicles (buses and cars)
on the ferry. Compute the mean for z.
D 100
3.5 vehicles
D 100
Consider a small ferry that can accommodate cars
and buses. The toll for cars is $3 and the toll for
buses is $10. Let x and y denote the number of
cars and buses, respectively, carried on a single
trip. Suppose that x = 2.8 and 2x = 1.66 and that
y = .7 and 2y = .61. Assume all events are
independent.
Let w= total amount of money collected in tolls.
Compute the mean for w.
D 200
$15.40
D 200
Consider a small ferry that can accommodate cars
and buses. The toll for cars is $3 and the toll for
buses is $10. Let x and y denote the number of
cars and buses, respectively, carried on a single
trip. Suppose that x = 2.8 and 2x = 1.66 and that
y = .7 and 2y = .61. Assume all events are
independent.
Let z= total number of vehicles (buses and cars)
on the ferry. Compute the standard deviation for z.
D 300
1.507 vehicles
D 300
Consider a small ferry that can accommodate cars
and buses. The toll for cars is $3 and the toll for
buses is $10. Let x and y denote the number of
cars and buses, respectively, carried on a single
trip. Suppose that x = 2.8 and 2x = 1.66 and that
y = .7 and 2y = .61. Assume all events are
independent.
Let w= total amount of money collected in tolls.
Compute the standard deviation for w.
D 400
$8.71
D 400
Gain Communications sells aircraft communications units to both
military and civilian markets. Next year’s sales depend on market
conditions that cannot be predicted exactly. Gain follows the
practice of using probability estimates of sales. These are the
personal probabilities that express the informed opinion of Gain’s
executives. Assume all events are independent.
Let X = the number of units sold estimated by the military division.
Let Y = the number of units sold estimated by the civilian division.
X
1000
p(X) .10
3000 5000
.30
.40
10,000 Y
.20
p(Y)
300
.40
500 750
.50
.10
Gain makes a profit of $2000 on each military unit sold and $3500
on each civilian unit sold.
Find the standard deviation of the total profits.
D 500
$5,606,737.58
D 500
Your track record of scores on English exams is
normally distributed with a mean of 35 and
standard deviation of 5. Your been informed if you
attempt the homework (when assigned) and study
prior to taking the exam, your score should
double.
Assuming you “do” as you are instructed, what
would be your expect value on your next English
exam?
E 100
70
E 100
HEB believes that in a dozen eggs, the
mean number of broken eggs is 0.6 with a
standard deviation of 0.5 eggs. You buy 3
dozen eggs without checking them. What is
the expected value of the total broken eggs
you would have? Assume all events are
independent.
E 200
1.8 eggs
E 200
Your track record of scores on English exams is
normally distributed with a mean of 35 and
standard deviation of 5. Your been informed if you
attempt the homework (when assigned) and study
prior to taking the exam, your score should
double.
Assuming you “do” as you are instructed, what
would be your standard deviation on your next
English exam?
E 300
10
E 300
HEB believes that in a dozen eggs, the
mean number of broken eggs is 0.6 with a
standard deviation of 0.5 eggs. You buy 3
dozen eggs without checking them. What is
the standard deviation of the total broken
eggs you would have? Assume all events
are independent.
E 400
.866 eggs
E 400
In the 4X100 medley relay event, four swimmers swim 100
yards, each using a different stroke. OHS team preparing for
the district championship
looks at the times, their swimmer have posted, and creates a
model based on the following assumptions:
 The swimmers’ performances are independent.
 The means and standard deviations of the times (in
seconds) are shown (in table).
What is the standard deviation for the relay team’s total time
in this event?
Swimmer
Mean
Stddev.
1. Backstroke
50.72
2. Breaststroke 55.51
3. Butterfly
49.43
4. Freestyle
44.91
0.24
0.22
0.25
0.21
E 500
.461 seconds
E 500
What were Mateo’s and Lexie’s
Halloween costumes?
F 500
Dinosaurs
F 500
When is Lexie’s birthday?
F 500
Valentine’s Day 2016
F 500
What is Lexie’s middle name?
F 500
Maria
F 500
What is Mateo’s middle name?
F 500
Luis
F 500
What is Mrs. Garcia’s middle name?
F 500
Eugenia
F 500