Chapter 6 MCQ Practice

A carnival game offers a $100 cash prize for anyone who can break a balloon by throwing a dart at it. It costs $8 to play and you're willing to spend up to $32 trying to win. You estimate that you have a 10% chance of hitting the balloon on any throw. Find the expected amount you will win. Assume that throws are independent of each other.

1. - $638.73

2. $9.27

3. $6.88

4. - $11.52

5. $14.88

3. $6.88

An insurance policy costs $140 per year, and will pay policyholders $12,000 if they suffer a major injury (resulting in hospitalization) or $7000 if they suffer a minor injury (resulting in lost time from work). The company  estimates that each year 1 in every 1800 policyholders will have a major injury and 1 in every 500 a minor injury. What is the company's expected profit on this policy?

1. $119.23

2. $25,099,996.40

3. - $238.44

4. $131.33

5. - $20.67

1. $119.23

A company is interviewing applicants for managerial positions. They plan to hire two people. They have already rejected most candidates and are left with a group of 7 applicants of whom 5 are women. Unable to differentiate further between the applicants, they choose two people at random from this group of 7. Let the random variable X be the number of men that are chosen. Find the expected value of X.

1. μ = 0.83

2. μ = 0.57

3. μ = 1.43

4. μ = 0.71

5. μ = 0.33 

2. μ = 0.57

A slot machine at a casino pays out an average of $0.92, with a standard deviation of $125. It costs a dollar to play. If a person plays 7 times, what are the mean and standard deviation of the casino's profit?

1. μ = $0.56, σ = $330.72

2. μ = $6.44, σ = $330.72

3. μ = $0.56, σ = $875

4. μ = $0.56, σ = $6125

5. μ = $0.56, σ = $8.75

1. μ = $0.56, σ = $330.72

Miguel buys a large bottle and a small bottle of juice. The amount of juice that the manufacturer puts in the large bottle is a random variable with a mean of 1024 ml and a standard deviation of 12 ml. The amount of juice that the manufactuer puts in the small bottle is a random variable with a mean of 508 ml and a standard deviation of 4 ml. Find the mean and standard deviation of the total amount of juice in the two bottles.

1. μ = 1532 mL, σ = 12.65 mL

2. μ = 1532 mL, σ = 16 mL

3. μ = 1143.08 mL, σ = 12.65 mL

4. μ = 513 mL, σ = 16 mL

5. μ = 1532 mL, σ = 160 mL

The amount of cereal that a manufacturer puts in its boxes of cereal is a random variable with a mean of 1022 g and a standard deviation of 11 g. The amount of cereal that Tyler eats for breakfst is a random variable with a mean of 61 g and a standard deviation of 5g. The amount of cereal that Tyler's wife, Suzanne, eats for breakfast is a random variable with a mean of 53 g and a standard deviation of 3 g. If Tyler and Suzanne open a new packet of cereal on Monday morning, find the mean and the standard of the amount of cereal remaining in the packet after one breakfast.  Assume that the amount that Tyler eats is independent of the amount Suzanne eats.

1. μ = 908 g, σ = 12.45 g

2. μ = 908 g, σ = 19 g

3. μ = 1136 g, σ = 3 g

4. μ = 908 g, σ = 9.33 g

5. μ = 1136 g, σ = 12.45 g

1. μ = 908 g, σ = 12.45 g

The amount of money that Maria earns in a week is a random variable with a mean of $960 and a standard deviation of $35. The amount of money that Elena earns in a week is a random variable with a mean of $830 and a standard deviation of $15. If the difference between Maria's weekly income and Elena's weekly income can be described by a Normal model, what is the probability that the difference M-E is at least $149.04? Assume that Maria's earnings are independent of Elena's earnings.

1. 0.691

2. 0.655

3. 0.309

4. 0.274

5. 0.345

3. 0.309

A random variable X has a probability distribution as follows:

X	0	1	2	3
P(X)	2k	3k	13k	2k

Where k is a positive constant. The probability P( X < 2.0) is equal to

1. 0.90

2. 0.25

3. 0.065

4. 0.015

5. 1.00

2. 0.25