Z-Scores
NormCDF
Normal Distribution General
Review: Unit 1
Review: Unit 2
100
What is the formula for z-score?
What is z=(x-mu)/(sigma)
100
Give the NormCDF formula.
What is \text{NormCDF}(mu,sigma,\text{LB, UB})
100
What is the best measure of center for a normal distribution?
What is Mean
100
What is undercoverage bias?
What is "Bias that results when there are parts of the population who are more/less likely to be selected".
100
What type of data is represented by numbers and have a meaningful average/ordering?
What is Quantitative Data.
200
What does the z-score tell us?
What is "the number of standard deviations above or below the mean a data value is".
200
What does NormCDF find?
What is "the proportion of data above, below, or between two points".
200
What is the best measure of spread for a normal distribution?
What is Standard Deviation
200
True or False? Explain.
The best sampling methods have low bias and high variance.
What is False. The best sampling methods should have both low bias and variance.
200
What shape is the following distribution?
What is Unimodal Skewed Right
300
Interpret the z-score in context:
A researcher is studying the weights of rats who help French chefs cook 5 star meals. He weighs Remi and finds that his weight has a z-score of -1.75.
What is "Remi's weight is 1.75 standard deviations below the mean weight of rats that help French chefs cook 5 star meals".
300
A cafe wants there lattes to have at least 125 ml of milk. They take an SRS of 40 lattes and find that they have a mean of 110 ml with a standard deviation of 20 ml. What proportion of lattes are below their desired threshold?
What is 0.7734 or 77.43%
300
What percentage of data falls within 2 standard deviations (both ways) of the mean?
What is 95%
300
What is the best way to ensure that your sampling method has as little bias as possible?
What is "Ensure the sampling method uses randomness in the selection, as this ensures less of our own biases control who gets selected".
300
If you have data with Q1=4 and Q3=13 , how large must a data value be to be considered an outlier on the upper side?
What is larger than 26.5
400
Burbank airport is doing research to prepare for the opening of their new terminal. They decide to look at the number of passengers that flew out of the terminal on 30 random days. They find a mean passenger amount of 11000 passengers, with a standard deviation of 700 passengers. Find and interpret the z-score for a day where there is 12000 passengers.
What is z approx1.43 which means "A day where Burbank airport has 12000 passengers is 1.43 standard deviations above the mean number of daily passengers at Burbank airport".
400
Monitoring temperatures in Antarctica is very important for ensuring there are no disastrous polar cap collapses. McMurdo finds that the average temperature near the station is about -4^oF with a standard deviation of 20^oF . Collapses usually occur at around 28^oF , what is the probability of a collapse occurring on a random day near McMurdo station?
What is 0.0548 or 5.48%
400
If you have a normally distributed variable with a mean of 20 and a standard deviation of 5, what percent of data is above 30?
What is 2.5%
400
What type of sampling method is shown below:
A researcher is trying to understand the snack buying habits of Chargers fans at SoFi stadium. They decide to separate the groups by section and then number each section. They draw 30 numbers using a random number generator and sample everyone in the chosen sections.
What is Cluster Random Sampling
400
If the distribution below represents income data of McDonald's Employees in SoCal and the IQR=4250 and sigma=3340 . Use CSOCS to describe the distribution. Assume no outliers.
C: Income data of McDonald Employees in SoCal.
S: Unimodal Skewed Right
O: None
C: Median = 27581
S: IQR = 4250
500
If you get a z-score of -1, which of the following statements is/are true?
A) Your value is 1 SD below the mean
B) Your SD is -1
C) 84% of data falls above this value
D) 84% of data falls below this value
E) Your value is an outlier
What is "A and C"
500
Real minted gold bars are legally required to be within 0.03% of their advertised weight. If 10oz minted gold bars have an average weight of 311.066 grams and standard deviation of 0.05 grams, what is the probability that a random gold bar is considered authentic?
What is 0.9380 or 93.80%
500
A company has created a water balloon that doesn't pop! The diameter of these balloons have a mean diameter of 15cm with a standard deviation of 1.5cm. What is the probability that a random water balloon has a diameter between 10.5cm and 16.5cm?
What is 83.85%
500
If we see a cause-and-effect relationship in an observational study, can we say that cause-and-effect relationship exists? Explain.
What is "No, only an experiment allows us to measure the direct effect of a variable changing. Thus we can only say they correlate in a observational study".
500
Use the following data collected on the price of orders at See's Candy, make a dotplot and then use CSOCS to describe its distribution.
3, 4, 4, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 8, 8, 9
C: Data collected on price of orders at See's Candy.
S: Unimodal Symmetric (Approximately Normal is also good)
O: None
C: Mean = $6
S: Standard Deviation = $1.58