VOCAB
PROBABILITY
NORM. DISTRIB.
Z-SCORE
BINOMIALS
100
A numerical outcome of a probability experiment is called a 
____________.
What is a random variable?
100
Describe the sample space for the following experiment
The roll of a die
There are six possible outcomes for the roll of a die: the numbers from 1 to 6. So a sample space is {1, 2, 3, 4, 5, 6}.
100
A normal distribution has mean u=59 and standard dev. o=20. Find and interpret the Z-Score for x=75
What is 0.80?
A normal value of 75 is 0.80 SD's above the mean.
100
A randomly selected woman has a height of x=67 inches. Find and interpret the z-score.
z-score= 1
The woman is 1 standard deviation about the mean, so she is taller than the average height of women by 1 SD.
100
Determine whether the probability is a binomial distribution.
A random sample of 250 voters is chosen from a list of 10,000 registered voters. Let X be the number who support the incumbent mayor for reelection.
What is yes?
200
As the sample size increases, the sample mean approaches the_________ mean.
What is population?
200
Determine whether the statement is true of false
For any event A, 0 ≤ P (A) ≤ 1.
True
200
If the area to the left of z=-a is 0.4, then the area to the right of z=-a is what?
What is 0.60?
200
A man has a height of -0.7 SD's below the mean. If you saw this man at walmart in a group of other men, how tall would he seem?
The man would look short because he is below the mean height of all men.
200
To find the mean of a discrete random variable, multiply each possible value of the random variable by its probability, then add the products.
True
300
The sum of all the probabilities in a discrete probability distribution must be equal to _________.
1
300
How likely is it for an event with a probability of 1.00 to occur?
Guaranteed!
300
A normal population has a mean of 9 and a standard deviation of 5.
What proportion of the population is less than 19?
What is 0.9772?
300
Compact fluorescent bulbs are more energy efficient than incandescent bulbs, but they take longer to reach full brightness. The time that it takes for a compact fluorescent bulb to reach full brightness is normally distributed with mean 29.8 seconds and standard deviation 4.5 seconds. A randomly selected bulb takes 28 seconds to reach full brightness. Find and interpret the z-score for x= 28.
z-score= -0.4
This randomly selected light bulb lights up faster than the mean by 0.4 SD's.
300
Determine whether the table represents a discrete probability distribution.
x p(x)
2.1 0.1
2.2 0.1
2.3 0.1
2.4 0.1
Does not represent a probability distribution; probabilities do not add up to 1.
400
___________ random variables can take on any value in an interval.
What is Continuous?
400
Who will you vote for? In a survey of 500 likely voters in a certain city, 275 said that they planned to vote to reelect the incumbent mayor.
What is the probability that a surveyed voter plans to vote to reelect the mayor?
275/500 = 0.55
400
A normal population has a mean of 9 and a standard deviation of 5.
What is the probability that a randomly chosen value will be greater than 4?
What is 0.8413?
400
A study reported that the length of pregnancy from conception to birth is approximately normally distributed with mean μ = 272 days and standard deviation σ = 9 days. What proportion of pregnancies last longer than 280 days?
p=0.1867
400
Blood types: The blood type O negative is called the “universal donor” type, because it is the only blood type that may safely be transfused into any person. Therefore, when someone needs a transfusion in an emergency and their blood type cannot be determined, they are given type O negative blood. For this reason, donors with this blood type are crucial to blood banks. Unfortunately, this blood type is fairly rare; according to the Red Cross, only 7% of U.S. residents have type O negative blood. Assume that a blood bank has recruited 20 donors.
a. What is the probability that two or more of them have type O negative blood?
b. What is the probability that fewer than four of them will have type O negative blood?
c. Would it be unusual if none of the donors had type O negative blood?
d. What is the mean number of donors who have type O negative blood?
e. What is the standard deviation of the number of donors who have type O negative blood?
a. 0.4131
b. 0.9529
c. No, P(0) = 0.2342.
d. 1.4
e. 1.1411
500
In a binomial distribution, there are _________ possible outcomes for each trial.
2
500
Determine whether events A and B are mutually exclusive
A: Sophie is a member of the debate team; B: Sophie is the president of the theater club.
What is not mutually exclusive?
500
The volume of beverage in a 12-ounce can is normally distributed with mean 12.06 ounces and standard deviation 0.04 ounce.
What is the probability that a randomly selected can will contain more than 12.08 ounces?
What is 0.3085?
500
Heights in a group of men are normally distributed with mean μ = 69 inches and standard deviation σ = 3 inches.
Find the height whose z-score is 1. Interpret the result.
Find the height whose z-score is −2.0. Interpret the result.
Find the height whose z-score is 0.6. Interpret the result.
1. 72 Inches Tall
2. 63 Inches Tall
3. 70.8 Inches Tall
500
Potholes: In a certain city, the number of potholes on a major street has a Poisson distribution with a rate of 3 per mile. Let X represent the number of potholes in a 2-mile stretch of road. Find
a. P(4)
b. P(More than 1)
c. P(Between 5 and 7 inclusive)
d. μX
e. σX
a. 0.1339
b. 0.9826
c. 0.4589
d. 6
e. 2.4495