Larget Statistics/Mathematics 309
Solution to Exam 2A
November 6, 2009
1. A bucket contains 3 red and 2 blue balls. A ball is drawn uniformly at random and replaced in the bucket.
This is repeated until each color appears at least once. Let X be the numbe
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Quiz 6.1A AP Statistics Name:
I. The probability distribution below is for the random variable X = number of mice caught in
traps during a single night in small apartment building.
-m
(a) Make a histogram of this probability distrib
Chapter 3
Section 3.1
Check Your Understanding, page 144:
1. The explanatory variable is the number of cans of beer. The response variable is the blood alcohol
level.
2. There are two explanatory variables: amount of debt and income. The response variable
Quiz 5.2A AP Statistics Name:
1. Suppose you choose a random US. resident over the age of25. The table below is a
probability model for the education level the selected person has attained, based on data from
the American Communit Surve from 20062008.
E
QumlA _ _ APmmw Fhmmf"
I. The probability distribution bemw is far the random variable X = number of mice caught in
traps during a single night in small apartment building
!
M ._ . g ;
3
(b) Describe, PU? :- 2 in words and nd its value.
F a?!" 5345'; 2.
Test 1A . AP Statistics . Name:
Part 1: Muitiple Choice. Circle the letter corresponding to the best matter.
1. The pie chart at right describes the distribution of state
tree types for the 50 states in the United States. The common
Spruce-tir-hemleck 5.0
Quiz 2.1A AP Statistics Name:
A Q new, , ,
group f 78 third- ade students in a Midwestern elementary school took a self-concept test
that meas well they felt about themselves. Higher scores indicate more positive self-
concepts. A histogram and some surmn
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uiz 1.1A 1 AP Statistics Name it?
Below rs some information about lms for the Best Movie Academy Awaid (Oscar) in 2609.
Budget Totai # of
(miliions of Oscar Running time _ MMPA
Name Genre doiiars) Nominations cfw_minutes Rating
Avatar Adventure 237 9
f ' . AP Statistics
1. A consumer watchdog organization estimates the mean weight of l-ounce Fun-Size candy
bars to see if customers are getting full value for their money. A random sample of 25 bars is
selected and weighed, and the organization reports t
Chapter 9
Section 9.1
Check Your Understanding, page 532:
1. (a) The parameter of interest is p = proportion of students at Jannies high school who get less than 8
hours of sleep at night. (b) The hypotheses are: H 0 : p = 0.85 and H a : p 0.85.
2. (a) Th
Chapter 12
Section 12.1
Check Your Understanding, page 750:
1. The scatterplot must show a linear pattern, the observations must be independent, the residuals need to
be approximately Normally distributed, the residuals must show roughly equal scatter for
Chapter 7
Section 7.1
Check Your Understanding, page 417:
1. The parameter is = 20 ounces of iced tea. The statistic is x = 19.6 ounces of iced tea.
2. The parameter is p = 0.10, or 10% of passengers. The statistic is p = 0.08, or 8% of the sample of
pass
'leettSA
Batu
1. n P[X21=1P[X= nrx=tj=ttfa_2-t+tt_3't=a_3a
1. I 2k+3k+13ir+2k=Lnei=.[tiPcfw_X<2]=P[X =l]erl)=5k=_25.
3. e [1&,0[_15+[jtltltl][.4)+(](_25+[5,)[.l)=itt.
4 Ir Binemial prebability fennula: Hi atmeeaam in n Iriala when p = aueeeaa in one trial
Practice 6.11 6.2 AP Statistics - Name:-
> 1. The probability distribution below is for the random variableX = number of medical tests
performed on a randomly selected outpatient at a certain hospital.
(a) Make a histogram df this probability distributi
STAT/MATH 309
1
Solution 2
Solutions for HW2
1:
P (A B C) = P (A B) + P (C) P (A B) C)
= P (A) + P (B) P (A B) + P (C) P (A C) (B C)
= P (A) + P (B) + P (C) P (A B) P (A C)
P (B C) + P (A B C)
2:(a)|S| = 620 , |A| = 20 518 P = |A| = .198
2
|S|
(b)P (atle
Larget Statistics/Mathematics 309
Solution to Exam 4A
December 14, 2009
1. Discrete random variables X1 , X2 , X3 , . . . are independent and identically distributed with these probabilities:
P (Xi = 0) = 0.6, P (Xi = 5) = 0.3, and P (Xi = 15) = 0.1.
(a)
Larget Statistics/Mathematics 309
Solution to Exam 1A
October 2, 2009
1. There are three fair 10-sided white dice with numbers 0, 1, 2, . . . , 9 and two fair regular 6-sided red dice with
numbers 1, 2, 3, 4, 5, 6. All ve dice are rolled. The die rolls ar
Larget Statistics/Mathematics 309
Solution to Exam 3A
November 30, 2009
Sheepshead is a popular card game in Wisconsin that uses a 32-card deck. There are two types of cards with
14 trumps and 18 nontrump cards. In the ve-handed version, the deck is well-
STAT/MATH 309
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Solution 4
Solutions for HW4
1: cfw_2,4,1 or cfw_2,4,6 or cfw_2,5,1 or cfw_2,5,6 or cfw_3,4,1 orcfw_3,4,6 or cfw_3,5,1 or cfw_3,5,6
2: P (W1 |W2 ) =
P (W2 |W1 )P (W1 )
P (W2 |W 1)P (W1 )+P (W2 |R1 )P (R1 )
=
(3/5)(2/3)
(3/5)(2/3)+(2/5)(1/2
STAT/MATH 309
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Solution 3
Solutions for HW3
1: (a)Dene An (x)= number of sequences of coin tosses length n where the longest fun of
heads is x or less
(b)P = A15 (5)A15 (4) = .0972
215
2: (a)P(two or more heads)=1P(no heads)-P(one head)= 1 0.54 + 4 0.54
STAT/MATH 309
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Solution 8
Solutions for HW8
1
1:(a)Since X and Y are independent, fX,Y (x, y) = fX (x)fY (y) = 24 xy 4 e(x+y) , x > 0, y > 0.
(b)W > 0, 0 < Z < 1
(c)X = W Z,Y = W (1 Z),|J| = W ,
1
1
fW,Z (w, z) = w 24 wzw4 (1 z)4 e(wz+w(1z) = 24 w6 z(1 z
STAT/MATH 309
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Solution 1
1.2.1
(a): P(cfw_1,2)=P(cfw_1)+P(cfw_2)=1/2+1/3=5/6
(b): P(cfw_1,2,3)=P(cfw_S)=1
(c): P(A)=1/2 if and only if A = cfw_2 or A = cfw_1, 3
2
1.2.4
P (cfw_2, 3) = P (cfw_2) + P (cfw_3) = 0.5 + 0.3 = 0.8 = 0.7
So the probability is n
STAT/MATH 309
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Solution 10
Solutions for HW10
3
1: EX = 0 xf (x)dx = 2
3
E(X 2 ) = 0 x2 f (x)dx = 30/7
V ar(X) = E(X 2 ) (EX)2 =2/7
2:Note that the standard normally distributed random variable is with mean 0 and variance
1.
E(S) = E(X) + E(Y ) = 0
E(D)