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Unformatted text preview: WorkSheet 7.1C ‘ AP Statistics Name: A small store keeps track of the number X of customers that make a purchase during the ﬁrst hour that
the store is open each day. Based on the records, X has the following probability distribution. X 0 i 2 3 4
P0!) 0.1 0.1 0.1, 0.1 0.6 1. What is the probability that no customers make a purchase during the ﬁrst hour that the store is open? (X: 03 Z a \ 2. What is the probability that the number of customers that make a purchase during the ﬁrst hour that
the store is open is more than 1 but no greater than 3? P[MX_":°>3: PCX‘N mixe3) :.lf—.l?iZ :2 ﬂt‘X23\ 2 .. Hal 3.2
3. Find the mean number of customers that make a purchase during the ﬁrst hour that the store is open. on” + H) +2.1 1L$fl 4—996: 4. Find the standard deviation of the number of customers that make a purchase during the ﬁrst hour
that the store is open. Of : (092M + (v33?! +.~<L"3>Z’("
“£5 ‘ a I ,__ .
6x @242 gxzﬁfw MW 5. Let the random variable X represent the proﬁt made on a randomly selected day by a certain store. Assume X is normal with a mean of $3 60 and standard deviation $50. The probability is
approximately 0.6 that on a randomly selected day the store will make less than xo amount of proﬁt. Find x0. ) v /
mmeOI/V‘ / (a):
X” 3&0 ,255’ Chapter 7 ’ £5 27,? The weight of mediumsized tomatoes selected at random from a bin at the local supermarket is a
random variable with mean it = 10 ounces and standard deviation 0‘ = 1 ounce.
O
6. Suppose we pick four to aloesl frdg the bin at random and put them in a bag. Let X = the weight
of the bag. Find the mean of the random variable, X. x : Afr/lmMM/Wy 5 LID 7. Calculate the standard deviation (in ounces) of X. 0 My . ( W
X i
A. L 7’ L1 .7/ K
52 r, x+\+\+\ ’ x W ZQaMpMWS . . . . om'bm‘k’b‘q
8. The weight of the tomatoes in pounds (1 pound = 16 ounces) IS a random variable, say Y.
Determine the standard deviation of Y. , . .
22¢ / it" ’2 i
.— . ,_/ ;— lO/g‘ézs f}; 2f [62 {e 9. Suppose we pick two tomatoes at random from the bin. The difference in the weights of the two
tomatoes selected (the weight of the ﬁrst tomato minus the weight of the Second tomato) is a
random variable, W. Find the mean and standard deviation (in ounces) of W. 05:3 [040 “I 095%)
[772,73 g: 0’”) : zit/,2 (.2 Chapter 7 Name: Date: Use the following to answer question 1: In a particular game, a fair die is tossed. If the number of spots showing is either 4 or 5 you win
$1; if number of spots showing is 6 you win $4; and if the number of spots showing is 1, 2, or 3
you win nothing. LetX be the amount that you win. 1. Referring to the information above, the expected value of X is
A) $0.
B) $1.
C) $2.50.
D) $4. Use the following to answer question 2: The weight of mediumsize tomatoes selected at random from a bin at the local supermarket is a
random variable with mean ,u = 10 ounces and standard deviation 0': ounce. 2. Suppose we pick four tomatoes from the bin at random and put them in a bag. The
weight of the bag is a random variable with a mean of
A) 2.5 ounces.
B) 4 ounces. C) 10 ounces. _
D) 40 ounces. Use the following to answer question 3: A small store keeps track of the numberX of customers that make a purchase during the ﬁrst
hour that the store is open each day. Based on the records,X has the following probability
distribution. X 0 1 2 3 4
P00 0.1 0.1 0.1 0.1 0.6 Page 1 3. Referring to the information above, the mean number of customers that make a purchase
during the ﬁrst hour that the store is open is
A) 2. 
B) 2.5.
C) 3.
D) 4. Use the following to answer question 4: Let the random variable X be a random number with the uniform density curve given below. 1.1311 9353 NI 4. Referring to the information above, P(0.7 <X < 1.1) has value
A) 0.30.
B) 0.40.
C) 0.60.
D) 0.70. 5. Suppose there are three balls in a box. On one of the balls is the number 1, on another is
the number 2, and on the third is the number 4. You select two balls at random and
without replacement from the box and note the two numbers observed. The sample
space S consists of the three equally likely outcomes {(1, 2), (1, 3), (2, 3)}.X, the total
of the two balls selected, has probabilities X 3 4 5
Probability 1/3 1/3 1/3
The probability thatX is at least 4 is
A) 0.
B) 1/3.
C) 2/3.
D) 1.0. Page 2 Use the following to answer question 6: The weight of mediumsize tomatoes selected at random from a bin at the local supermarket is a
random variable with mean ,u = 10 ounces and standard deviation 0: ounce. 6. The weight of the tomatoes in pounds (1 pound = 16 ounces) is a random variable wit
standard deviation '
A) 1/16 pounds. B) 1 pound.
C) 16 pounds.
D) 256 pounds. 7. I roll a fair die and count the number of spots on the upward face. A fair die is one for
which each of the outcomes 1, 2, 3, 4, 5, and 6 are equally likely. According to the law
of large numbers
A) several (four or ﬁve) consecutive rolls for which the outcome 1 is observed is
impossible in the long run. If such an event did occur, it would mean the die is no
longer fair. B) after rolling a 1, you will usually roll nearly all the numbers at least once before
rolling a 1 again. C) in the long run, a 1 will be observed about every sixth roll and certainly at least once
in every 8 or 9 rolls. D) none of the above is true. Use the following to answer question 8: Let the random variableX be a random number with the uniform density curve given below. an GE} LG 8. Referring to the information above, P(X = 0.25) is
A) 0.00.
B) 0.25.
C) 0.75.
D) 1.00. Page 3 Use the following to answer question 9: The weight of mediumsize tomatoes selected at random from a bin at the local supermarket is a normal randOm variable with mean y = 10 ounces and standard deviation 0= 1 ounce. Suppose
we pick two tomatoes at random from the bin, so the weights of the tomatoes are independent. 9. Referring to the information above, the difference in the weights of the two tomatoes
selected (the weight of ﬁrst tomato minus the weight of the second tomato) is a random
variable with which distribution? A) N(0, 0.5). B) N(O, 1.41). C) N(0, 2). D) uniform with mean 0. Use the following to answer question 10: A small store keeps track of the numberX of customers that make a purchase during the ﬁrst
hour that the store is open each day. Based on the records,X has the following probability
distribution. X o 1 2 3 4
P00 0.1 0.1 0.1 0.1 0.6 10. Referring to the information above, the standard deviation of the number of customers
that make a purchase during the ﬁrst hour that the store is open is
A) 1.4.
B) 2.
C) 3.
D) 4. Use the following to answer question 11: Let the random variable X represent the proﬁt made on a randomly selected day by a certain
store. Assume X is normal with a mean of $360 and standard deviation $50. Page 4 11. Referring to the information above, the probability is approximately 0.6 that on a
randomly selected day the store will make less than
A) $347.40.
B) $0.30.
C) $361.30.
D) $372.60. Use the following to answer question 12: The probability density of a random variableX is given in the ﬁgure below. 12. Referring to the information above, the probability thatX is at least 1.5 is
A) 0.
B) 1/4.
C) 1/3.
D) 1/2. Use the following to answer question 13: Suppose there are three balls in a box. On one of the balls is the number 1, on another is the
number 2, and on the third is the number 3. You select two balls at random and without
replacement from the box and note the two numbers observed. The sample space 8 consists of
the three equally likely outcomes {(1, 2), (l, 3), (2, 3)}. LetX be the total of the two balls selected. 13. Referring to the information above, the mean of X is
A) 2.0.
B) 14/6.
C) 4.0.
D) 26/6. Page 5 14. A fourthgrade teacher gives homework every night in both mathematics and language
arts. The time to complete the mathematics homework has a mean of 10 minutes and a
standard deviation of 3 minutes. The time to complete the language arts assignment has
a mean of 12 minutes and a standard deviation of 4 minutes. The time to complete the mathematics and the time to complete the language arts homework have a correlation p
= —0.75. The standard deviation to complete the entire homework assignment is
A) 16 minutes.
B) 5 minutes.
C) 4 minutes.
 D) 3 minutes. Use the following to answer question 15: The weight of mediumSize tomatoes selected at random from a bin at the local supermarket is a normal random variable with mean [1 = 10 ounces and standard deviation 0': 1 ounce. Suppose
we pick two tomatoes at random from the bin, so the weights of the tomatoes are independent. 15. Referring to the information above, the probability that the difference in the weights of
the two tomatoes exceeds 2 ounces is
A) 0.0170.
B) 0.0340.
C) 0.0680.
D) 0.1587. Use the following to answer question 16: The weight of mediumsize tomatoes selected at random from a bin at the local supermarket is a
random variable with mean ,u = 10 ounces and standard deviation 0': ounce. 16. Suppose we pick four tomatoes from the bin at random and put them in a bag. The
weight of the bag is a random variable with a standard deviation (in ounces) of
A) 0.25.
B) 0.50.
C) 2.
D) 4. Page 6 17. Suppose we have a loaded die that gives the outcomes 1—6 according to the probability
distribution X l 2 3 4 5 6
P(X) 0.1 0.2 0.3 0.2 0.1 0.1 Note that for this die all outcomes are not equally likely, as they would be if this die
were fair. If this die is rolled 6000 times, then A", the sample mean of the number of spots
on the 6000 rolls, should be about A) 3. B) 3.30. C) 3.50. D) 4.50. 18. A random variable X has mean ﬁx and standard deviation ox. Suppose n independent
observations of X are taken and the average X of these n observations is computed. If n is
very large, the law of large numbers implies A) that A" will be close to ,UX.
B) that X will be approximately normally distributed. C) thatthe standard deviation of X’ will be close to 0X.
D) all of the above. 19. Suppose X is a random variable with mean ﬁx and standard deviation ox. Suppose Y is a
random variable with mean ﬂy and standard deviation 0?. The mean of X + Y is
A) #X + W
B) (ﬁx/0X) + (,uY/
C) ,UX + ﬂy, but only if X and Y are independent.
D) (/lX/OX) + (yr/0y), but only if X and Y are independent. Use the following to answer question 20: A psychologist studied the number of puzzles subjects were able to solve in a ﬁveminute period
while listening to soothing music. LetX be the number of puzzles completed successfully by a
subject. The psychologist found thatX had the following probability distribution. Value of X 1 2 3 4
Probability 0.2 0.4 0.3 0.1 Page 7 20. Referring to the information above, the mean number of puzzles completed successfully,
ﬁx, is
A) 1.
B) 2.
C) 2.3.
D) 2.5. Chapter 7: Random Variables Page 8 / Practice Test 7A AP Statistics Name: Directions: Work on these sheets. Part 1: Multiple Choice. Circle the letter corresponding to the best answer. 1. A random variable Y has the following distribution: 3C ,‘rg C 1» ' kt 4. , 1 Y —1 o 1 2 .
P(Y) 3e 2e 0.4 0.1 55 +,S 2: 1 The value of the constant C is: SC .’
(b) 0.15
(c) 0.20 I C t . )
(d) 0.25 (e) 0.75 2. A random variable X has a probability distribution as follows:
r O l 2 3 P(r) 2k 3k‘ 13k 2k 
.I .13 Gas i
Then the probability that P(X < 2.0) is equal to f
(a) 0.90 K ’ ’ 05’
0.25 ‘3 p c0.65 P(xro mxzh : firm 2.2;“
(d) 0.15
(e) 1.00 3. Cans of soft drinks cost $ .30 in a certain vending machine. What is the expected value and
variance of daily revenue (Y) from the machine, if X, the number of cans sold per day has
M ; E(X)= 125, and Var(X)=50? “
7C (a E = 37.5 Var Y) = 50 '5'] ( ’1 g)?“ (50>Q
(b) E(Y) = 37.5, Var(Y) = . ’ ‘
c . , ar — _
EEd) E(Y) = 37.5, Var(Y) = 15
(e) E(Y) = 125, Var(Y) = 4.5 4. A rock concert producer has scheduled an outdoor concert. If it is warm that day, she expects to
make a' $20,000 proﬁt. If it is cool that day, she expects to make a $5,000 proﬁt. If it is very cold
that day,m suffer a $12,000 less, Based upon historical records, the weather ofﬁce has
estimated the chances of a warm day to be .60; the chances of a cool day to be .25. What is the
producer's expected proﬁt?
(a) $5,000
(b) $13,000
(c) $15,050 (d Chapter 7 1 ' ll Ll 0 Test 7C 5. In a particular game, a fair die is tossed. If the number of spots showing is either 4 or 5 you win
$1, if number of spots showing is 6 you win $4, and if the number of spots showing is 1, 2, or 3 you win nothing. Let The expected value of X is (a)$0.00. .
\l 370 M 8L; C 2.50. (d) $4.00. I L I
@%m. P0 Questions 6 and 7 use the following: Suppose X is a random variable with mean rm and standard
deviation 6X. Suppose Y is a random variable with mean W and standard deviation 6y. 6. The mean of X + Y is (a) up" it? (b) (MX/ 610+ (HY/ Gr) (c) uX+ uy, but only if X and Y are independent. (d) (uX/ 0X) + (uy/ 6y), but only if X and Y are independent.
(e) None of these. 7. The variance of X + Y is (a) OX + (5y. (b) <ch + (on? (C) ox + cry, b ( (6X) 7+ (092, but only if X and Y are independent. I.
e None 0 t ese. 8. Suppose X is a continuous random variable taking values between 0 and 2 and having the
probability density function below. '4: 3 P(1 EX 5 2) has value (a) 0.50. N _ (b)0.33 9(35X513'éé,17:r,2;
' (d) 0.00 (e) None of these. Chapter 7 2 Test 7C Part 2: Free Response
Answer completely, but be concise. Write sequentially and show all steps. 9. Nevins Partners is planning a major investment. The amount of proﬁtX is uncertain but a
probabilistic estimate gives the following distribution (in millions of dollars): I
m (a) Find the mean proﬁt ux and the standard deviation of the proﬁt. 695* q 2 0‘6 3 rixhiw , *1 .
éKXL‘Pbi/(lx :5 O: =€(yfﬂ‘73 'R I (5’ :26?!) (b) Nevins Partners owes its source of ca ital a fee of $200,000 plus 10% ,f the roﬁ So the ﬁrm actually retalns Y = 0.9X— 0.2 from the investment. Find the mean and standard deviation
of Y.
7» 2 .
ND: Marat ; ’CHBBP’Z 53: 0,9st 1‘ ﬂak/53 g 2
M3: 95 “(mm 03: SEWSS
0:75, : ’3 2):ze7ﬁzx;s7mw 10. Slot machines are now video games, with winning determined by electronic random number
generators. In the old days, slot machines were like this: you pull the lever to spin three wheels;
each wheel has 20 symbols, all equally likely to show when the Wheel stops spinning; the three
wheels are independent of each other. Suppose that the middle wheel has 9 bells among its 20
symbols, and the left and right wheels have 1 bell each among its 20 symbols. .z" 7' 6 wheels stop w1th exactly 2 bells showing? Chapter 7 3 ' Test 7C bat. Could a .300 year just be luck? Typical major leaguers bat about 500 times a season, and hit
about .260. A hitter’s successive tries seem to be independent. So the number of hits in a season 11. A study of the weights of the brains of Swedish men found that the we' ; Chapter 7 ' w. k a random
variable with mean 1400 grams and standard deviation 20 grams. Fi ‘
such that Y = a + bX has mean 0 and standard deviation 1. M? Moo 0} a 20 en a baseball player hits .300, everyone applauds. A .3 00 hitter gets a hit in 30% of times at should have th ' omial d'stribution with n = 500 and — 0.26. Calculate the probability that a
randomly sel cted layer h ts .3 00 in a season. ' rcade game. Glenn likes the game at the state fair where you toss a coin into a saucer. You win
f the coin comes to rest in the saucer without sliding out the other side. Glenn has played this
game many times and has determined that on average he wins one out of every 12 times he plays.
He believes that his cha f winning are the same for each to ‘ novreason to think that
lenn believes that this o be sure that the probability of
d the smallest number A for which P(X > A) < 0.05. I pledge that I have neither given nor received aid on this test. 4 . Test 7c ...
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 Spring '11
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