Variables and Data Organization
Empirical Rule and Data Shapes
Misc.
Standard Normal Distribution and Binomial Experiments
Probability
100
Is the variable qualitative, quantitative, or constant? If qualitative, is it binary:
Height of students in the class
Quantitative
100
According to the Empirical Rule, approximately what percent of data is within 2 standard deviation from the mean?
95%
100
A medicinal study of the effect of meditation on memory is being conducted. Participants take a memory test in the morning and at night. One group is meditating during the day, and one is not meditating during the day.
Which is the explanatory variable and which is the response variable?
Explanatory: meditation (yes or no)
Response: memory test results
100
72% of U.S. employees have access to medical care benefits. You randomly select 9 employees. Find the probabilty that exactly 6 of access to medical care.
25.69%
9C6 (.72)^6 (.28)^3
100
There are 8 marbles in a bag, 4 red, 3 green and 1 blue. What is the probability of picking a green marble and then a blue without replacement?
3/56=.05367=5.4%
(3/8)(1/7)=3/56
200
Is the variable qualitative, quantitative, or constant? If qualitative, is it binary:
What month you were born in.
Qualitative
200
Which Brand has the smallest IQR?
Brand B
200
What is the advantage of a double blind study over a blind study?
A double blind reduces bias more, as the researcher AND the subjects do not know who has the treatment and who has the placebo.
200
IQ scores generally follow a normal distribution with a mean of 100 and a standard deviation of 16.
What percent of people’s IQs would you expect to be under 90?
.2643
zscore=-.625=-.63
200
Find the number of 3 person teams you can create from a group of 8 people.
56
8C3
300
Give an example of a qualitative, binary, variable.
passing test. attending school/not attending school.
300
If the data set is skewed left, what would be a better measure of center, mean or median? AND WHY?
Median, it is resistant to outliers where the mean will be less than the median.
300
Your English teacher weights your grades as follows: 20% classwork, 30% projects, 30% tests and 20% quizzes. If you have a 82 in classwork, 95 in projects, 80 in tests, and 78 in quizzes, what is your final average?
84.5
82(.2)+95(.3)+80(.3)+78(.2)
16.4+28.5+24+15.6
300
What are the two main factors in determining whether a situation is a "binomial experiment"?
Independent trials
Only 2 possible outcomes (success/failure)
300
How many distinguishable ways can the letters in the word ONOMATOPOEIA be written?
9,979,200
12!/(4!2!)
400
Given the 5 number summary, is there an outlier? If so, is it a high or low outlier?
min: 1 Q1: 9 Med: 12 Q3: 15.25 Max: 26
yes, the max is an outlier
400
Jill scored a 85% on her math test and Bill scored a 90% on his math test. If Jill's test had an average of 88% and a standard deviation of 2, while Bill's test had an average of 93 with a standard deviation of 1.25, who did better on their exam comparatively?
Jill! Her z-score is -1.5. Bill's z-score is -2.4.
400
What is the probability of choosing someone who prefers Baseball, given they are female.
23/36
63.89%
400
The amounts of time per workout an athlete uses a stair-climber are normally distributed, with a mean of 20min and a standard deviation of 5min. Find the probability that a randomly selected athlete uses a stair-climber for between 20 and 28min.
.4452
(28-20)/5 =1.60 -> .9452
(20-20)/5 = 0.00 -> .5000
.9452 - .5000 = .4452
400
Using the digits 3, 4, 5, 6, and 7, how many even 3 digit numbers can be formed such that there are no repeating digits in the number?
24
4*3*2
500
What is wrong with this stem and leaf plot?
There is no key included!
500
A manufacturer of calculators keeps track of length of time it takes before a product is returned for repair. They find the mean is 985 days and the standard deviation is 83 days. What percentage of calculators need to be repaired between 902 and 1151 days?
81.5%
95-68=27/2=13.5
68+13.5=81.5
500
At a fundraiser, 500 tickets are sold at $1 each for the following prizes: $1,000, $500, $250, and $100. You buy one ticket. Find the expected value and interpret whether that is a gain or a loss.
$2.70 gain
1000(1/500)+500(1/500)+250(1/500)+100(1/500) =3.7
3.7-1=2.7 gain!
500
IQ scores generally follow a normal distribution with a mean of 100 and a standard deviation of 16.
What score do the top 10% of people score?
120.48
.8897->1.28=(x-100)/16
20.48=x-100
500
Jeff hangs out with his friends 45% of the time on Saturdays. If Jeff hangs out with friends, the probability of him eating dinner with them is 60% and if he does not hang out with them, the probability of him eating dinner with them is 10%.
What is the probability that Jeff will hang out with his friends and not eat dinner with them?
18%
1-.6=.4
(.45)(.4)=.18