Algebra 2 Unit 8 - Statistics Packet - Dam

UNIT 8:
Statistics

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SUCCESS CRITERIA

I can… find the mean and standard deviation of a set of data & use them to draw a representative normal curve.

I can explain… what a confidence interval means for a given scenario.

I can justify… why certain sampling methods are biased.

I can apply… statistical methods to analyze real-life scenarios.

LESSON TABLE OF CONTENTS PG #
8.1 3-4
8.2 TITLE 5-6
8.3 Sampling Methods 7-9
8.4 Calculator Statistics 10
8.5 Normal Distribution (Empirical Rule & Z-Scores) 11-12
Normal Distribution (Area)
Confidence Intervals 2

Lesson 8.1 - Data Collection & Sampling Methods

Population
Sample

Identify the population and sample for each scenario.
1) In a city, a survey of 3257 adults ages 18 and over found that 2605 of them own a tablet.

2) To find out the consumers’ response towards a new flavor for sports drinks, a company surveys
1000 athletes who drink sports drinks and find that 726 of them like the new flavor.

Sampling Methods

Individuals are randomly selected from the population to be in the sample
Individuals from the population volunteer to be in the sample
Individuals who are easy to reach are selected from the population to be in the sample
Individuals are selected from the population using a rule (i.e., every other person)

Individuals are randomly selected from each strata, which are created by dividing the
population based on shared characteristics

Individuals are selected by randomly selecting one cluster from a group of clusters,
which are created by dividing the population into small groups

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Identify the sampling method for each scenario.
3) A restaurant owner wants to know whether the customers are satisfied with the service. Every fifth

customer is surveyed.
4) A company manager wants to determine whether the employees are satisfied with the employee

lounge. The manager surveys the employees who are in the lounge during her lunch time.
5) A state survey is conducted to find out how many households own more than one vehicle.

Households are divided into north, east, south, and west regions of the state. Households are then
randomly surveyed from each region.

Bias

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Lesson 8.2 - Calculator Statistics

What do each of the following represent?

Standard Deviation

Find the answer to each equation while listing the steps involved.

1) For the following set of data, find the population standard deviation, to the nearest hundredth.

120, 157, 134, 141, 131, 124, 136, 154, 132

Steps: Population Standard Deviation:

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2) For the following set of data, find the sample standard deviation, to the nearest hundredth.

Steps: Sample Standard Deviation:

3) For the following set of data, find the number of data within 1 population standard deviation of the mean.

58, 63, 68, 69, 75, 66, 65

Steps: # of data within 1 population
standard deviation of the mean:

4) For the following set of data, find the percentage of data within 2 population standard deviations of
the mean, to the nearest 10th of a perce

Steps: % of data within 2 population
standard deviations of the mean:

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Lesson 8.3 - Normal Distribution (Empirical Rule & Z-Scores)
Normal Distribution

Empirical Rule

Based on the empirical rule, what percent of data is…
1) Greater than the mean?
2) Between the mean and 2 standard deviations below the mean?
3) More than 2 standard deviations above the mean?

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Answer the following questions using the empirical rule.
1) IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.

What percentage of people have an IQ score between 70 and 130?

2) When Juan commutes to work, the amount of time it takes him to arrive is normally distributed
with a mean of 29 minutes and a standard deviation of 3.5 minutes. Determine the interval that
represents the middle 68% of his commute times.

3) When Piper runs the 400 meter dash, her finishing times are normally distributed with a mean of
84 seconds and a standard deviation of 2.5 seconds. Determine the interval of times that
represent the middle 99.7% of her finishing times in the 400 meter race.

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Z-Score Data Value Z-Score

1) On a standardized exam, the scores are normally distributed with a mean of 300 and a standard
deviation of 25. Find the z-score of a person who scored 250 on the exam.

2) On a standardized exam, the scores are normally distributed with a mean of 300 and a standard
deviation of 50. Find the z-score of a person who scored 325 on the exam.

3) On a standardized exam, the scores are normally distributed with a mean of 200 and a standard
deviation of 29. Find the z-score of a person who scored 235 on the exam.

4) On a normally distributed test, a score of 34 falls one standard deviation below the mean, and a
score of 46 falls one standard deviation above the mean. Determine the mean of this test.

5) On a normally distributed test, a score of 47 falls two standard deviations below the mean, and a
score of 71 falls one standard deviation above the mean. Determine the mean of this test.

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Lesson 8.4 - Normal Distribution (Area)

1) At a local restaurant, the amount of time that customers have to wait for their food is normally
distributed with a mean of 16 minutes and a standard deviation of 5 minutes. What is the
probability that a randomly selected customer will have to wait between 5 minutes and 16 minutes.
Round to the nearest thousandth.

2) The amount of time a certain brand of light bulb lasts is normally distributed with a mean of 900
hours and a standard deviation of 70 hours. What percentage of light bulbs lasts less than 980
hours. Round to the nearest tenth.

3) When Justin runs the 400 meter dash, his finishing times are normally distributed with a mean of
69 seconds and a standard deviation of 1.5 seconds. What percentage of races will his finishing
time be slower than 72 seconds. Round to the nearest tenth.

4) Haily earned a score of 630 on Exam A that had a mean of 550 and a standard deviation of 40.
She is about to take Exam B that has a mean of 400 and a standard deviation of 100. How well
must Hailey score on Exam B in order to do equivalently well as she did on Exam A? Assume the
scores on both exams are normally distributed.

5) When Jaxson goes bowling, his scores are normally distributed with a mean of 200 and a
standard deviation of 14. Out of the 100 games that he bowled last year, how many of them would
he be expected to score between 164 and 188. Round to the nearest whole number.

6) For males in a certain town, the systolic blood pressure is normally distributed with a mean of 135
and a standard deviation of 10. If 176 males from the town are randomly selected to participate in
a study, how many of them would be expected to have a systolic blood pressure less than 119.
Round to the nearest whole number.

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Lesson 8.5 - Confidence Intervals
Confidence Interval

1) A study was commissioned to find the mean weight of the residents in a certain town. The study
found the mean weight to be 187 pounds with a margin of error of 3 pounds. Write a confidence
interval for the true mean weight of the residents of the town.

2) A study was conducted to determine the mean SAT scores of the graduating high school seniors
in a certain state. The study found a confidence interval for the mean score to be between 497
and 555. What is the margin of error on the survey?

3) A survey was given to a random sample of the residents of a town to determine whether they
support a new plan to raise taxes in order to increase education spending. The percentage of
people who favored the plan was 36%. The margin of error for the survey was 1.5%. What is a
reasonable value for the actual percentage of residents that support the tax plan?

4) A survey was given to a random sample of 25 votes in the United States to ask their preference
for a presidential candidate. Of those surveyed, 20 respondents said they preferred Candidate A.
At the 95% confidence level, what is the margin of error for this survey expressed as a proportion
to the nearest thousandth?

5) A survey was given to a random sample of 25 residents to determine whether they support a new
plan to raise taxes. Of those surveyed, 76% said they were in favor of the plan. At the 95%
confidence level, what is the margin of error for this survey expressed as a percentage to the
nearest tenth?

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6) A study was conducted to determine the mean SAT scores of the graduating high school seniors
in a certain state. The study examined a random sample of 74 graduating seniors and found the
mean score to be 458 with a standard deviation of 104. At the 95% confidence level, find the
margin of error for the mean, rounding to the nearest tenth.

7) A study was commissioned to find the mean weight of the residents in a certain town. The study
examined a random sample of 63 residents and found the mean weight to be 192 pounds with a
standard deviation of 33 pounds. At the 95% confidence level, find the margin of error for the
mean, rounding to the nearest tenth.

8) A study of a local high school tried to determine the mean amount of money that each student had
saved. The school surveyed a random sample of 90 students and found a mean savings for
$5000 with a standard deviation of $1300. Determine a 95% confidence interval for the mean,
rounding to the nearest whole number.

9) A survey was given to a random sample of 95 voters in the United States to ask about their
preference for a presidential candidate. Of those surveyed, 60% said they preferred Candidate A.
Determine a 95% confidence interval for the percentage of people who prefer Candidate A,
rounding to the nearest tenth.

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