Function Junction
To determine if a graph represents a function, what line test do you use?
Vertical Line Test
Which type of random variable can assume a countable number of values (e.g., number of siblings)?
Discrete Random Variable
What is the total area under the Normal Curve?
1
What is the area under the normal curve to the left of the mean (z = 0)?
0.5 (or 50%)
What is the probability of an event that is impossible to happen?
0 (or 0%)
Evaluate the function
f(x) = 2x² − 3 at x = 2
5
The sum of the probabilities of all values of a random variable must equal what number?
1
In a standard normal distribution, the mean is equal to what number?
0
If the area to the left of z = 1 is 0.8413, what is the area to the right of z = 1?
0.1587 (Solution: 1 - 0.8413)
If the probability that it will rain tomorrow is 0.3, what is the probability that it will NOT rain?
0.7 (Complement Rule: 1 - 0.3)
If f(x) = x + 1 and g(x) = 2x, what is (f + g)(x)?
3x + 1
What is another term for the "mean" of a discrete probability distribution?
Expected Value (or Expectation)
According to the Empirical Rule, approximately what percent of data falls within 1 standard deviation of the mean?
68%
The area under the curve corresponds to what mathematical concept starting with "P"?
Probability
A box contains 3 red balls and 2 blue balls. If you pick one ball at random, what is the probability that it is blue?
2/5 or 0.4 or 40%
This type of function is defined by different formulas for different parts of its domain.
Piecewise Function
If the probability of getting Heads is 0.5, what is the expected number of Heads in 10 tosses?
5
What is the formula for calculating the Z-score?
z = (x̄ - μ) / σ or z = (x - μ) / σ
If a student scores in the 99th percentile, what percent of the students did they score higher than?
99%
If P(A) = 0.4 and P(B) = 0.5, and the events are Mutually Exclusive (they can't happen at the same time), what is the probability of A OR B?
0.9
If f(x) = 2x and g(x) = x + 5, find the composite function (f∘g)(x)
2x + 10 (Solution: f(x+5) = 2(x+5))
This statistical term describes how "spread out" the values of a random variable are from the mean.
Variance or Standard Deviation
If a Z-score is negative, the raw score is located where relative to the mean?
Below the mean or to the left of the mean
To find the area between two z-scores (e.g., between z = 1 and z = 2), what operation do you perform on their individual areas?
Subtraction (Subtract the smaller area from the larger area).
If you flip a coin twice, what is the probability of getting two Heads (Head AND Head)?
1/4 or 0.25 or 25%