Probability Distributions Mean & Expectation Variance & Std. Dev. Binomial Distribution (no calc) Binomial Distribution (with calc) 1 pt 1 pt 2 pt 2 pt 3 pt 3 pt 4 pt 4 pt 5 pt 5 pt 1
Is the following a probability distribution? X P(X) 0. 125 1. 375 2. 375 3. 125 2
Yes, since 0 < P(X) < 1 and The sum of P(X) is 1 3
Joe plans to flip a coin 3 times in a row. Let the random variable be number of tails. Make a probability distribution table. 4
X P(X) 0 1/8 1 3/8 2 3/8 3 1/8 5
Fill in the missing probability: X 1 P(X). 18 2. 21 3. 23 4 5. 21 6
. 17 7
Lydia rolls one six sided die. Create a probability distribution in which the random variable is the possible outcomes. 8
X 1 2 3 4 5 6 P(X) 1/6 1/6 1/6 9
Construct a probability distribution for drawing a card from a deck of 30 cards consisting of 14 cards numbered 1, 10 cards numbered 2, 5 cards numbered 3, and 1 card numbered 4. 10
X 1 P(X) 14/30 2 3 4 10/30 5/30 11
Find the mean of the probability distribution. X 1 2 3 4 5 P(X). 18. 21. 23. 17. 21 12
Mean = 3. 02 13
A contractor has a 65% chance of making $45, 000, a 20% chance of losing $30, 000 and a 15% chance of breaking even. What is the expected value? 14
$23, 250 15
A raffle has two prizes: $500 and $100. Each ticket costs $5. 1000 tickets are sold and you buy 3 tickets. What is the expected value? 16
-$13. 25 17
A company manufactures calculators in batches of 5 and there is a 5% rate of defects. Find the mean number of defects per batch. 18
Mean = 0. 25 19
In a sample of 40 Internet users, a survey showed that 61% are somewhat concerned about the confidentiality of their email. Find the mean number of people who are NOT concerned with the confidentiality. 20
15. 6 21
Compute the variance: X 0 1 2 3 4 P(X). 18. 44. 27. 08. 03 22
0. 92 23
Compute the standard deviation: X 0 1 2 3 4 P(X) 0. 1 0. 2 0. 3 0. 2 24
1. 25 25
A study found that 1% of Social Security recipients are too young to vote. If 800 Social Security recipients are randomly selected, find the variance of the number of recipients who are too young to vote. 26
7. 92 27
Find the standard deviation for the number of heads when 20 coins are tossed. 28
2. 24 29
If 3% of calculators are defective, find the variance and standard deviation of a lot of 300 calculators. 30
8. 73, 2. 95 31
A company manufactures calculators in batches of 5 and there is a 5% rate of defects. Find the probability of getting exactly 3 defects in a batch. 32
N=5 X=3 P =. 05 Q =. 95 P(exactly 3 heads) =. 001 33
The percentage of American men who say they would marry the same woman if they had to do it all over again is 80%. The percentage of American women who say they would marry the same man again is 50%. What is the probability that in a group of 10 married men, at least 8 will claim they would marry the same woman again? 34
. 677 35
Have you ever purchased an article of clothing, worn it once, and then returned it? This is called a “one-time fling”; about 10% of adults have deliberately done this and feel no guilt. In a group of 7 adult friends, what is the probability that no more than 2 people have done a “one-time fling”? 36
. 974 37
In Manitoba, 5% of fish that were caught and released died. Suppose that a group of anglers caught and released 16 fish in Manitoba. What is the probability that all of the fish lived? 38
. 440 39
Richard has just been given a 10 -multiple choice quiz in history class. Each question has 5 possible answers. Assuming that Richard guesses on all 10 questions, find the probability that he will answer all questions incorrectly. 40
0. 107 41
A fair quarter is flipped 3 times. Find the probability of getting exactly 3 heads. 42
. 125 43
Approximately 10% of the population has blood type B. Suppose we choose 12 people at random from the population and test the blood type of each. What is the probability that exactly 3 of these people have blood type B? 44
0. 085 45
Privacy is a concern for many users of the Internet. One survey showed that 59% of Internet users are somewhat concerned about the confidentiality of their e-mail. Based on this information, what is the probability that for a random sample of 40 users, 20 are concerned about the privacy of their email? 46
. 065 47
A social scientist claims that only 60% of all high school seniors who are capable of doing college work actually go to college. If this is true, find the probability that among 10 capable seniors, at least 8 will go to college. 48
. 167 49
A research team at Cornell University conducted a study showing that approximately 10% of all businessmen who wear ties wear them so tight that they actually reduce blood flow to the brain. At a board meeting of 20 businessmen, all of whom wear ties, what is the probability that no more than 3 ties are too tight? 50
. 867 51
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