Download 7.2 More Problems - Mrs. McDonald

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7.2 More Problems
AP Statistics
1. A particular golf club has a form of gambling available to players called “Pulltabs.” A player pays $1 to pull a small
paper ticket off a spindle, open it, and examine the four-digit number inside. If the last digit of the four-digit number is
“1,” “2,” “3,” “4,” “5,” “6,” “7,” “8,” or “9,” the player wins nothing. If the last digit is a “0,” the player wins a golf ball.
However, if the last two digits are both “0,” the player wins a dozen golf balls. If the value of a gold ball is $2, what is
the expected gain/loss in monetary value from buying one Pulltabs ticket?
a. A loss of about $0.48
b. A loss of about $0.58
c. A loss of about $0.99
d. A gain of about $0.42
e. Approximately break even – no gain, no loss
2. A company markets 16-ounce bottles of jam. The mean amount of jam per bottle is 16 ounces, with a standard
deviation of 0.1 ounces. The mean weight of the glass bottles holding the jam is 5 ounces, with a standard deviation
of 0.5 ounces.
a. What is the mean weight of a filled bottle?
b. What is the standard deviation of the weight of a filled bottle?
c.
When shipped to stores, 12 bottles are packed randomly in each box. What is the mean and standard deviation
of the weights of these random groupings of 12 bottles?
d. The mean weight of the empty boxes is 50 ounces, with a standard deviation of 4 ounces. What are the mean
weight and the standard deviation of the weights of the filled boxes?
e. If the amount of jam per bottle, the weight of the bottles (with their lids), and the weight of the boxes are
approximately normally distributed, what percent of boxes will weigh more than 320 ounces?
3. A particular college entrance exam has two parts: math and verbal. The distribution of math score M has a mean of
500 and a standard deviation of 100. The distribution of verbal scores V also has a mean of 500 and a standard
deviation of 100. What is the average combined score (math + verbal) on the exam? What is the standard deviation
of the combined score?
4. American adult males have heights that are distributed with a mean of 173 cm and a standard deviation of 7.5 cm.
American adult females have heights that are distributed with a mean of 161 cm and a standard deviation of 6.5 cm.
If one male and one female are randomly selected from the population, what is the average difference in their
heights? What is the standard deviation of the differences in their heights?
5. A brand of model rocket kit, when finished, produces rockets with a mean mass of 134 grams and a standard
deviation of 4.0 grams. The model rocket engine required to fly the rocket is purchased separately and has a mass
with mean 36 grams and standard deviation 2.0 grams. If a randomly selected engine is inserted into a randomly
selected rocket, what are the mean and standard deviation of the total mass?
6. A prestigious private school offers an admission test on the first Saturday of November and the first Saturday of
December each year. In 2002, the mean score for hopeful students taking the test in November (X) was 156 with a
standard deviation of 12. For those taking the test in December (Y), the mean score was 165 with a standard
deviation of 11. What are the mean and standard deviation of the total score X + Y of all students who took the test in
2002?
7. Sophia was recently promoted to assistant manager at a small women’s clothing store. One of her duties is to fill out
order forms for women’s shirts, which come in size 6, 7, 8, 9, 10, 11, and 12. She would like to determine how many
shirts of each size to order. At first, she thought of ordering exactly the same number of shirts from each of the
available sizes, but the she decided against doing that, because there might be a greater demand for certain sizes
than for others. She looked up sales receipts from the past three months and summarized the information as follows:
Shirt Size
6
7
8
9
10
Number sold 85
122
138
154
177
a. Prepare a probability distribution of the number of shirts sold for each size.
11
133
b. What is the probability that a randomly selected customer will request a shirt of size at least 11?
c.
Compute the expected shirt size of a random shopper and the standard deviation of the shirt size.
d. If Sophia plans to order a total of 1000 shirts, how many shirts of size 8 should she order?
12
92
7.2 More Problems – Answers
1.
A
2.
hmmmm
a.
b.
P(X=-1) = 0.90; P(X=23) = 0.01; P(X=1) = 0.09 E(X) = 0.90(-1) + 0.09(1) + 0.01(23) = -0.58.
16 + 5 = 21 ounces
0.12  0.5 2 = 0.51 ounces
c.
21 + 21 + 21 + … + 21 = 252 ounces; = 1.766 ounces
d.
252 + 50 = 302 ounces;
e.
N(302, 7.31)… P (C  320)  P Z 
6.12 2  4 2 = 7.31 ounces


There is a mistake
here…use what we
did in class.
320  302 
  P( Z  2.46)  1  P( Z  2.46)  0.0069 ….69% of the
7.31 
boxes will weigh more than 320 ounces.
3.
500 + 500 = 1000; the scores are NOT independent, therefore we can’t find the st dev of the combined scores
4.
173 – 161 = 12 cm; 7.52 + 6.52 = 98.5…9.9 cm
5.
weights are independent of each other because they are selected randomly. 134 + 36 = 170 grams (mean);
4.0 2  2.0 2  20  4.47 grams (st dev)
6.
we will assume that X & Y are independent: 156 + 165 = 321;
7.
hmmmm
a.
0.09, 0.14, 0.15, 0.17, 0.20, 0.15, 0.10 etc.
b.
0.25
c.
E(X) = 9.09
d.
1000(0.15) = 150 shirts of size 8
st dev. = 1.84
12 2  112  265  16.28