Q5

1. What is the variance of the following probability distribution?

x

0

1

2

3

4

P(x)

0.2

0.3

0.15

0.3

0.05

1. What value would be needed to complete the following probability distribution?

x

0

1

2

3

4

P(x)

1/3

1/8

0

1/4

1/6

1. A box contains ten $1 bills, six $5 bills, and four $10 bills. A person is charged $5 to select a bill. What is the expected value?

2. What is the standard deviation of the following distribution?

x

5

6

7

8

9

P(x)

0.12

0.27

0.34

0.22

0.05

1. If approximately 3% of adults cut their sandwiches into squares before eating them, what is the probability that in a group of 150 people, exactly 3 would cut their sandwiches into squares before eating them?

2. A binomial distribution has n = 5, p = 0.35. Find P(x = 2 successes).

3. You just bought 1 raffle ticket for $2.00. If 400 tickets are sold at $2.00 each for a prize of $250, what would be your expected winnings?

4. If I deal you one card from a standard deck of 52 and it is a face card, I will give you a $5.00 bill. There are 12 face cards. There is one catch: You have to pay me something to play this game. How much would that be if the game is to be fair?

5. A person flips a coin 6 times. Let "x" be the number of tails. Which of the following values could not be a value of "x" for this experiment?

6. What is the mean of the following probability distribution?

x

8

10

12

14

P(x)

0.20

0.30

0.10

0.40

1. 2500 tickets are sold for $1.00 each for one cash prize of $250, one cash prize for $100, one cash prize for $50, and one cash prize for $25. What is the expected value if a person purchases 5 tickets?

2. Find the standard deviation of the following probability distribution.

x

1

2

3

4

5

P(x)

0.15

0.32

0.28

0.15

0.10

1. The probability that a federal income tax return will have 0, 1, or 2 errors is 0.85, 0.1, and 0.05 respectively. If 1000 federal income tax returns are checked, about how many errors would you expect altogether?

2. Find the mean of the following probability distribution.

x

0

1

2

3

4

P(x)

0.18

0.33

0.27

0.16

0.06

1. The failure rate for taking the bar exam in Boston is 35%. If 250 people take the bar exam, what is the standard deviation for the number of failures?

2. Using the binomial formula, find P(x = 4 successes) if n = 8 and p = 0.32?

3. At a computer component manufacturing plant, 2% of the hard drives will fail within 90 days. In a sample of 250 hard drives, what is the probability that at least one will fail within 90 days?

4. If you roll a pair of regular 6-sided dice and get a sum of 9, you are given a $10 bill. If you get a sum of 3, you are given a $50 bill. The cost to play the game is $2. What would be your expected winnings?

5. If n = 10, p = 1/8, find P(x = 3 successes).

6. If 60% of all households own DVD players, what is the probability that if 11 households are selected at random, exactly 6 will own DVD players?