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Normal Distribution
Regression Equations
Permutations and Combinations
Basic Probability
Binomial Probability and Expected Value
100
Given an approximately normal distribution with a mean of 175 and a standard deviation of 37. What percent of values are within the interval (101, 249)?
95%
100
Write the equation for a parabola, given that the points (0,2), (-1,9) and (3,5) are on the graph.
y=2x^2-5x+2
100
A particular new car model is available with 5 choices of color, 3 choices of transmission, 4 types of interior, and 2 types of engine. How many different variations of this model car are possible?
120
100
Example 1: P(Sophomore and <10 hours/week)
5.0% 52/1046
100
A fair coin is tossed five times. On each toss, the probability of a head is 1/2, and the five tosses are all independent events. What is the probability that exactly two of the five coin tosses produced a head?
31.25%
200
Given an approximately normal distribution with a mean of 122 and a standard deviation of 22. What interval contains 68% of all values?
(100, 144)
200
Write a power regression equation that contains the points (4, 16) and (9,54).
y=2(x^1.5)
200
There are five members of the Math Club. In how many ways can the positions of officers, a president and a treasurer, be chosen?
20
200
Example 1: What is the probability of selecting someone who works 10 to 20 hours per week, given that they are a senior?
44.4% 110/248
200
A fair coin is tossed five times. On each toss, the probability of a head is 1/2, and the five tosses are all independent events. What is the probability that exactly one of the five coin tosses produced a tail?
15.63%
300
The EPA fuel economy estimates for automobile models tested recently predicted a normal model with a mean of 24.8 mpg and a standard deviation of 6.2 mpg. If 2,000 cars are tested, how many would have a fuel economy between 18.6 mpg and 31.0 mpg?
1364
300
The following data represents (hours past, bacteria present): (0,20), (1,40), (2, 75), (3,150), (4,297), (5,510). Which model is better, power or exponential? Explain your reasoning.
Exponential because the r^2 is closer to 1 than the r^2 value for the power model.
300
There are five members of the math club. In how many ways can the two person Social Committee be chosen?
10
300
Example 10: How many students did not vote for either dance?
128
300
An unfair coin is weighted so that the probability of a head is 1/3 and the probability of a tail is 2/3. The coin is tossed seven times, and the outcome on each toss is independent of that on all of the other tosses. What is the probability of exactly two heads?
30.73%
400
The EPA fuel economy estimates for automobile models tested recently predicted a normal model with a mean of 24.8 mpg and a standard deviation of 6.2 mpg. What percentage of vehicles would have a fuel economy between 20 mpg and 30 mpg?
57.98%
400
An object is dropped off a bridge. The following coordinates represent (time in seconds, height above ground in feet): (0, 50), (0.2, 49.4), (.6, 44.3), (1.2, 27.0). Find the appropriate regression equation to model this situation.
y=-16.11x^2+0.17x+50.00
400
How many different 12-person juries (6 male and 6 female) can be chosen from a pool of 12 males and 9 females?
77616
400
Example 9: At some universities, you must score a 4 or higher to be awards credit. What is the probability of a random student scoring 4 or higher?
42%
400
An unfair coin is weighted so that the probability of a head is 1/3 and the probability of a tail is 2/3. The coin is tossed seven times, and the outcome on each toss is independent of that on all of the other tosses. What is the probability of more than two tails?
95.47%
500
Some IQ tests are standardized to a Normal model with a mean of 100 and a standard deviation of 16. The top 10% of all scores represent the label of “genius”. What is the range of scores for anyone who qualifies as a genius?
Greater than 120.5
500
The value of a car depreciates over time. The following data represents (years owned, value of car): (0,24000), (2, 19111), (6, 11902), (10,7502) Find an appropriate regression equation and determine the value of the car in 8 years. (Side note: Interpolation or Extrapolation?)
9459.38
500
How many more ways can 10 International Club members running for the positions of president, vice president, and secretary be selected when compared to 5 Beta Club members running for 2 identical positions of club representative?
710
500
Example 9: 282,814 students took the AP Calculus AB Exam in May of 2013. How many students were not eligible to receive credit at a school that required a score of 3 or higher?
114,822
500
Your company plans to invest in a particular project. There is a 35% chance that you will lose $30,000, a 40% chance that you will break even, and a 25% chance that you will make $55,000. What is the expected value?
3250