Data, Normal Distributions and Statistical Inference: Algebra 2 Math Quiz – PDF Download
Ten multiple-choice questions check the main ideas: standard deviation, the 68-95-99.7 rule, z-scores, study design and margin of error. Pick the one best answer for each question, then read the explanation to see the typical mistake.
🎯 Data, Normal Distributions and Statistical Inference – Algebra 2 math quiz
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Question 1
Values are approximately normal with mean 60 and standard deviation 5. What percent of values lie between 55 and 65?Mean 60, standard deviation 5.
A\(68\%\)
B\(34\%\)
C\(95\%\)
D\(50\%\)
Question 2
A student scores 92 on a test with mean 80 and standard deviation 8. What is the z-score?
A\(z=12\)
B\(z=0.67\)
C\(z=-1.5\)
D\(z=1.5\)
Question 3
Every value in a data set with mean 20 and standard deviation 4 is increased by 10. What are the new mean and standard deviation?
Amean 30, SD 4
Bmean 30, SD 14
Cmean 20, SD 14
Dmean 30, SD 40
Question 4
About what percent of a normal distribution with mean 500 and standard deviation 50 lies in the shaded region above 600?Mean 500, standard deviation 50; the tail above 600 is shaded.
A\(2.5\%\)
B\(5\%\)
C\(13.5\%\)
D\(16\%\)
Question 5
Researchers randomly assign 50 patients to take either a new medicine or a placebo and compare recovery times. What kind of study is this?
Aa sample survey
Ban experiment
Can observational study
Da census
Question 6
A study finds that students who eat breakfast have higher grades. The students chose whether to eat breakfast. Which conclusion is justified?
AEating breakfast causes higher grades.
BEating breakfast is associated with higher grades.
CSkipping breakfast lowers grades.
DEvery student should eat breakfast.
Question 7
A poll reports that 54% of voters support a measure, with a margin of error of 4 percentage points. Which statement is best supported?
AExactly 54% of all voters support it.
BThe poll proves that most voters support it.
CAt most 4% of voters oppose the measure.
DThe true percent is plausibly from 50% to 58%.
Question 8
A teacher wants to survey 40 of her 800 students. Which method gives a random sample?
ASurvey the first 40 students who enter the cafeteria.
BSurvey the 40 members of the chess club.
CNumber all students and pick 40 numbers with a random number generator.
DSurvey the 40 students who answer an online post.
Question 9
The histogram shows 200 simulated sample percents. The shaded bars, the middle 95% of results, run from 31% to 50%. What is the estimated margin of error?200 simulated samples of 100 people.
Aabout 19 percentage points
Babout 40 percentage points
Cabout 4.75 percentage points
Dabout 9.5 percentage points
Question 10
Why do researchers use random assignment in an experiment?
AIt guarantees that the results apply to a whole population.
BIt makes the sample size larger so the margin of error is zero.
CIt makes the groups comparable so differences can be credited to the treatment.
DIt lets participants choose the treatment they prefer.
🎉 Quiz complete!
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Remember:
Standards S-ID.A.4, S-IC.A.1, S-IC.B.3 and S-IC.B.4: normal models, z-scores, study design and margin of error.
Normal data follow the 68-95-99.7 rule: \(68\%\), \(95\%\) and \(99.7\%\) within 1, 2 and 3 standard deviations.
The z-score is \(z=\frac{x-\mu}{\sigma}\); the table gives the area to the left of \(z\).
Only an experiment with random assignment can support a cause-and-effect conclusion.
A margin of error can be estimated as half the width of the middle \(95\%\) of simulated sample results.
