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Winter 2010 Final #1
(1) [6.1/6.5] There are 10 homes in a Singles Only community…and it happens that there
are an equal number of males and females in the community…but they do not all get
cable, to be exact there are 2 men and 2 women that do not get cable. How many get
cable? So show me the Venn Diagram for the above information.
(2) [6.1/6.5] Given the following…complete the Venn Diagram:
U = 40, A = 17, B = 25, C = 20, A∩B = 8, C∩B = 15, A∩C = 7, (AUBUC)c = 2
What is the value of A∩B∩C? Show the Venn Diagram.
(3) [6.1] Given the following Venn Diagram…answer the following
Z
a
b
c
d
e
f
g
h
B
Yi
j
k
m
l
A
a) Y?
b) n(A)?
c) A∩B?
d) BUY?
e) (A∩B)c∩Z
f) Are there any subsets that are mutually exclusive?
(4) [6.2] A computer has 4 options for RAM, 3 options for hard drives, 2 possible
monitors to choose from, and 4 software packages from which to choose…
How many possible different computer packages could you create?
(5) [6.4]You have a 4-sided die that has the letters A, B, C, D on it and a standard 6-sided
die…
a) What is the sample space?
Sample Final
Math 130 (All) Winter2010
b) What is the subset of even numbers?
c) What is the subset containing “A” and odd numbers?
(6) [6.6] What is the probability of drawing one card from a standard deck and it being…
(a) a black card (b) a Jack or an Ace (c) a King and a Heart
(7) [6.7]Of the last 50 visits to Ellensburg the wind was blowing 35 times…
What is the probability that it will be a calm day on the next visit?
(8) [7.1]Out of a class of 10 students (6 are female)…choose a 4-person committee..
(a)
How many ways can this be done?
(b)
How many ways can you have a committee with less men than women?
(c)
What is the probability of having an all male committee?
(9) [7.1]Out of the above class of 10 (problem #8), you chose a committee with 2 females
in it…now choose a President, Vice-President and Secretary…
How many ways can this be done?
(10)
[7.1]What is the probability of a 5-card hand containing 2 pairs (neither are Aces)
and an Ace?
[7.2]How many different permutations can you have from the word “mixologist”?
(11)
(12)
[7.3/7.4/7.5]You have 4 bullets in your Colt 45 (the chamber holds 6, and you do
not know which ones are empty)…you give the chamber a spin and pull the trigger
twice…
(a)
What is the probability of clicking on two empty chambers?
(b)
What is the probability of clicking on an empty chamber given that the first
pull fired?
(c)
What is the probability that the first clicked on an empty chamber given that
the second pull fired?
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Math 130 (All) Winter2010
[7.6]Give me the reliability of the following systems…
(13)
(14)
[7.6]I want a stereo to be at least 99% reliable. How do I do that if I know
that my component reliability is only 75%?
(15)
[6.6]What is the probability of drawing a single card that is either a Jack
or a Spade?
(16)
[8.1/8.2/8.3]If the bag has 4 red marbles, 3 blue marbles and 2 green
marbles, and you choose 2 marbles…
(a)
What is the probability distribution, if Y is the number of red marbles?
(b)
What is the expected value of Y?
(c)
What is the variance?
(d)
What is the standard deviation?
(17)
[8.3]I have lost my data! I know that I had a mean of 155 and a standard
deviation of 3, but I do not have any idea of about how many would be walking
past my spot.
Could you tell me about what probability it would be if greater than 165 passed
by?
(18)
[8.4]I am flipping an unfair coin 12 times (P[heads] = 0.68…what is the
probability of getting…
(a)
Exactly 6 heads?
(b)
At least one tail?
(c)
What is the mean for this scenario?
(d)
What is σ for this scenario?
(19)
(a)
(b)
(c)
(d)
Sample Final
[8.4]Flip a fair coin 20 times…
P[heads>5]?
P[heads>3]?
P[heads<7]?
P[4<heads<8]?
Math 130 (All) Winter2010
(20)
[8.5]Using the following graph of a continuous random variable, find the
probability for:
0.20
0.12
1
(a) P[x = 4.7]
2
3
(b) P[x<5]
4
5
(c) P[x>5.5]
6
7
(d) P[3.2<x<4.5]
(21)
[8.6/8.7]Find the probability for a normal distribution, with a mean of 100
and a variance of 25, for the following
(a)
P[X>97]?
(b)
P[99<X<107]?
(c)
P[101<X<107]?
(22)
[8.6/8.7]Now using the same normal distribution from problem #21,
determine the score that cut off the…
(a)
Lower 33%?
(b)
Upper 50.8%?
(23)
[8.8]If you toss an unfair coin (where you get heads only 35% of the time)
150 times, what is the probability of getting less than 48 heads?
(24)
[9.1-9.4]Given the following …
11, 12, 22, 32, 54, 55, 64, 74, 50, 82, 60, 5, 52, 45, 66
(a)
Create a stem and leaf
(b)
Tally/Relative Frequency Chart (5 classes)
(c)
Range?
(d)
X-bar?
(e)
Approximate S using range
(f)
Sample Standard Deviation
(g)
Tukey’s 5-number Summary
(h)
Box’n Whisker plot
(i)
Are there any outliers
(25)
[9.5]Gas in the state of Washington has been averaging $2.80/gallon, with
a variance of 25 cents. If you took a sample of the prices of 100 gas stations, find
the probability that the sample mean would be…
(a)
Greater than $2.81?
(b)
Between $2.799 and $2.809?
Sample Final
Math 130 (All) Winter2010
(26)
[9.6]If a candidate’s crew took a survey of what people thought was the
percentage of the population was for the increase in military strength in
Afghanistan…the crew contacted 10,000 people and received a average of 55%
with a standard deviation of 2%…based on this…
What is expected mean percentage given by a 92% confidence interval?
(27)
[9.7]A recent survey showed that showed that 288 out 400 people on
campus respond with a smile when smiled at…setting a 97% confidence
interval…
What is true proportion of those returning smiles?
(28)
[10.1]There is a game in which, two dice are thrown (one red and one
blue). You win $10 if the two dice match; you win $5 if the red die comes up
even (but not matching), but you lose $3 for anything else…you also pay $1 to
play.
(a)
What is the net expected outcome?
(b)
What would the “pay to play” have to be to make it a fair game?
(c)
Instead of changing the $1 to play, what would you have to change the
$3 to in order to make it fair?
(29)
[10.3]Given the following...
Rain
Baseball
-500
Basketball
750
(a)
(b)
(c)
(d)
(26)
Demand
Probability
No Rain
500
-600
What is Optimists’ decision?
What is Pessimists’ decision?
What is Regretter’s decision?
What is the Bayesian decision? (45% chance of rain)
[10.4]For the following Demand/Probability Table…
8
.11
9
.21
10
.27
11
.28
12
.13
Cost: $5
Sales Price: $7
Salvage: $2
(a) What is the best inventory level?
(b) What is the expected profit for stocking 10?
(c) What is the expected profit on the 9th item?
Sample Final
Math 130 (All) Winter2010