Bruce is going to call one person from his contacts at random. He has 25 total contacts. 20 of those contacts are from his neighborhood. What is the probability that he calls a person not from his neighborhood?
5/25 = 0.2
100
My friend flips a fair coin. She pays me $10 if it lands on heads, and I pay her $6 if it lands on tails. What is the expected value of the amount of money I make?
$2
100
If the standard deviation of a given data set is equal to zero, what can we say about the data values included in the given data set?
They are all the same
100
The scores of an IQ test are normally distributed. The mean IQ score is 100 and the standard deviation is 15. What percentage of the population has an IQ between 85 and 115?
68%
100
What is the mean and standard deviation of a standard normal distribution?
mean = 0, SD = 1
200
If I roll a fair 6-sided die, what is the probability that I roll an odd number? (Odd means NOT divisible by 2)
P(odd) = 1/2
200
On flying to and from New York, I have calculated the following probabilities. The probability that I get to New York on time is 2/3, the probability that I get to New York
1 hour late is 1/6, the probability that I get to Denver 2 hours late is 1/12, and the probability
that I get to New York 3 hours late is 1/12. What is my expected value of lateness?
7/12
200
We have 3 sets of numbers. A = (9, 10, 11, 7, 13). B = (10, 10, 10, 10, 10). C = (1, 1, 10, 19, 19). Which set of numbers has the highest standard deviation?
C
200
Molly earned a score of 940 on a national achievement test. The mean test score was 850 with a standard deviation of 100. What is the z-score of Molly's test score?
z = 0.90
200
There is a party tonight. If my crush goes to the party, then there is a 90% chance that I will go too. If my crush doesn’t go to the party, then there is only a 50% chance that I will go. I find out that there is a 40% chance that my crush will go to the party tonight. Now what is the probability that I will go?
66%. 0.4 * 0.9 + 0.6 * 0.5 = .36 + .3 = .66
300
Which of the following statements are true?
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A) The probability that a continuous random variable takes on any single given value is 0.
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B) The area under the curve of the probability distribution of a continuous random variable depends on the variance of the random variable.
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C) A discrete random variable can only take distinct, separate values.
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D) A continuous random variable X can take an infinite number of values on an interval.
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E) The probability distribution for a discrete random variable looks like a smooth curve.
A) True. B) False. C) True. D) True. E) False
300
A company makes electronic gadgets. One out of every 50 gadgets is faulty, but the company doesn't know which ones are faulty until a buyer complains. Suppose the company makes a $3 profit on the sale of any working gadget, but suffers a loss of $80 for every faulty gadget because they have to repair the unit. On average, what is the profit per gadget produced?
$1.34
300
What is the variance of this data set? 2, 3, 6, 8, 11
10.8
300
A fair die is rolled 3 times. What is the probability that exactly one of the rolls is a 5? (Answer as a product of terms)
3 * (1/6) * (5/6)^2
300
The mass of baby elephants is normally distributed. The mean mass is 20 kg and the standard deviation is 6. If I have a baby elephant that is 29 kg, what is the z-score of its mass? How would I find the percentage of baby elephants that weigh less than 29 kg?
Z-score: 1.5. Look up P(Z < 1.5) in the standard normal distribution table.
400
I flip 3 fair coins. What is the probability that I get exactly 2 tails?
3/8
400
You and your friend are playing the following game: two dice are rolled; if the total showing is divisible by 3, you pay your friend $6. How much should he pay you when the total is not divisible by 3 if you want to make the game fair? A fair game is one in which your expected winnings are $0.
$3
400
In our workplace, we know everyone's monthly salary. 5 people make $3500, 8 people make $4000, 5 people make $4200, and 2 people make $4300. What is the standard deviation of the salaries of the 20 people? (rounded to an integer)
282
400
You measure speeds of cars on the highway. The speeds are normally distributed with a mean of 90 km/hr and a standard deviation of 10 km/hr. What is the probability that a car picked at random is traveling at more than 100 km/hr? (Answer as an integer)
16%
400
What is the variance of the first 10 natural numbers? (1, 2, 3, …, 8, 9, 10)
8.25
500
I roll two 6-sided dice. What is the probability that the sum is between 6 and 8?
(5 + 6 + 5)/36 = 16/36 = 4/9
500
The night watchman in a factory cannot guard both the safe in back and the cash register in front. The safe contains $6000, while the register has only $1000. Tonight the guard fears a robbery; the probability that the thief will try the cash register is 0.8 and the probability the thief will try the
safe is 0.2. If the guard is not present, the thief will take all the money. If the guard is present, the thief will go away empty handed. Where should the guard be positioned in order to minimize the thief’s gains?
The guard should be at the safe. Then the expected loss for the factory is $800 (rather than $1200)
500
A given data set has a mean μ and a standard deviation σ.
a) What are the new values of the mean and the standard deviation if the same constant k is added to each data value in the given set? Explain.
b) What are the new values of the mean and the standard deviation if each data value of the set is multiplied by the same constant k? Explain.
a) mean = μ + k. SD = σ. --- b) mean = k*μ. SD = k*σ
500
Bob only answers his phone 30% of the time. If you try to call Bob 6 times, what is the probability that he will pick up exactly 2 times? (Answer as a product of terms)
15 * (0.3)^2 * (0.7)^4 = 9.7%
500
You are taking a 30 question, multiple choice test (5 choices per question). The directions say that your grade will equal the number of correct answers minus 1/4 of the number of wrong answers. You are sure you have 20 of the answers correct. On each of the remaining 10 questions, you can definitely eliminate two of the choices. If you choose from the remaining three responses at random, what is your expected grade for the entire test? (out of 30)