Download S.ID.A.4 Assessment Items - Howard County Public School System

Algebra II Items to Support Formative Assessment
Unit 5: Inferences and Conclusions from Data
Summarize, represent, and interpret data on a single count or measurement variable.
S.ID.A.4 Use the mean and standard deviation of a data set to fit it to a normal distribution and to
estimate population percentages. Recognize that there are data sets for which such a procedure is
not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal
curve.
S.ID.A.4 Task
Hollywood made quite a few movies in 2011. The estimated production cost of some of the 2011
movies are listed below in millions of dollars.
Apollo 18
5
The Ides of March
The Roommate
16
Limitless
Our Idiot Brother
27
8
Friends With Benefits
Bad Teacher
35
20
Midnight in Paris
Diary of a Wimpy Kid 2:
Rodrick Rules
Footloose
The Help
17
21
Source Code
Bridesmaids
32
32.5
40
27
Horrible Bosses
Scream 4
Abduction
35
60
35
Final Destination 5
Spy Kids: All The
Time in the World
Paul
Season Of The Witch
Red Riding Hood
25
32
93
95
Johnny English Reborn 45
Super 8
50
The Beaver
79
No Strings Attached
The Tree of Life
Rise of the Planet of the
Apes
Zookeeper
Rio
Hop
Gnomeo and Juliet
Take Shelter
Percy Jackson & The
Olympians:
The Lightning Thief
Never Back Down 2:
The Beatdown
Twilight: Breaking
Dawn
Red State
36
71
53
Moneyball
49
Battle: Los Angeles
70
109
The Adjustment
Bureau
Vanishing on 7th
Street
Trespass
Hesher
48
Immortals
68
57
Mission Impossible
65.5
Mars Needs Moms
Dylan Dog: Dead of
Night
The Big Year
The Artist
52.5
51
55
57
Fast Five
Kung Fu Panda 2
63
61
Waiting For Forever
The Company Men
52.4
75
Take Me Home Tonight
The Amazing Mathemelion
72.5
91
54
51
15
12.5
42.5
41
42
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24
25
85
87
63
1. Construct a histogram representing the data above.
2. What can you conclude about Hollywood movie budget (i.e. distribution, mean, standard
deviation)? Support your answer using mathematics.
3. You along with your friends Ben and Matt are looking to pitch your original screenplay to a
few large Hollywood production companies. You proposed a 74.5 million dollar budget. What
percent of movies in 2011 spent less than your proposal?
4. Your original budget proposal of 74.5 million dollars was rejected by production companies.
You learned that small indie movies have a better chance of being picked up if 16.6% of the
movies cost less than yours to produce. Approximate the movie budget that is appropriate for
your movie.
Answer:
1.
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2. Hollywood movie budget in 2011 is an approximately normal distribution. The mean is
approximately 48.67 million dollars and the standard deviation is approximately 24 million
dollars.
3. z=1.08, approximately 85.99% of movies cost less than the proposal budget to produce.
4. A proposed budget of 25.39 million dollars will make the movie more likely to be picked up
by production companies. Students may work in reserve using the z table to find the
corresponding z score then calculate the budget value.
S.ID.A.4 Item 1
According to research conducted in 2010, the time that teenagers spend on their phones each day
follows a Normal distribution with a mean time of 111 minutes and a standard deviation of 28
minutes. Sue spends an average of 139 minutes on her phone a day. Kendra spends only 55
minutes on her phone each day. Dontrell spends 128 minutes on his phone each day.
a. What percentage of teens spend more time than Sue?
b. What percentage of teens spend less time on their phones than Kendra does?
c. What percentage of teens spend less time on their phones than Dontrell does? Give the zscore as well as the percentage.
Answers:
a. Using the 68-95-99.7% rule, 16%.
b. Using the 68-95-99.7% rule, 2.5%.
c. z=0.25, using the z-table 59.87%
S.ID.A.4 Item 2
A sample of sandwiches from fast food restaurants was selected and the calories of the
sandwiches are represented in the histogram below. The mean number of calories is 450 calories
with a standard deviation of 200 calories.
Part A
Color in all the bars of the histogram that represent the rounded number of calories of a fast food
sandwich in the sample that are within 1.5 standard deviations from the mean number of calories
of a fast food sandwich.
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http://mrnussbaum.com/graph/histogram/
Part B
Use the histogram to estimate the number of fast food sandwiches in the sample with calories
few than 1.5 standard deviations below the mean.
Answer:
Part A
Color in the boxes between 150 and 750.
Part B
Two sandwiches in this sample had fewer calories than 1.5 standard deviations below the mean.
S.ID.A.4 Item 3
You and your partner were assigned to estimate the mean and standard deviation of the Section
6.2 quiz grade distributions for 4 class periods. The grade distributions are represented by the
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following dot plots. Your partner wants to use the Empirical Rule for all 4 distributions. Do you
agree with this approach? Explain your reasoning.
Period 1
Period 2
Period 3
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Period 4
Answer:
The Empirical Rule can only be used to estimate mean and standard deviation for approximately
normal distributions. The period 4 grade distribution is the only one that can be estimated using
the Empirical Rule.
S.ID.A.4 Item 4
The distribution of heights of adult American males ages 20 years and over is approximately
normal with a mean of 69.3 inches and a standard deviation of 2.5 inches.
Part A
Draw a normal curve and label the mean and points one, two, and three standard deviations
above and below the mean.
Part B
a. What percent of men are taller than 71.7 inches?
b. Between what heights do the middle 95% of men fall?
c. What percent of men are shorter than 63 inches?
Answers:
Part A
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under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
Part B
a. Using the empirical rule 68-95-99.7, 16%
b. The heights are between 64.3 and 74.3 inches.
c. 𝑧 =
63−69.3
2.5
= −2.52; 0.59% of men are shorter than 63 inches.
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product
under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.