Pre-Requisite Probability

Prob #2: Suppose that the probabilities that an answer can be found on Google is 0.95, on Answers.com is 0.92, and on both websites is 0.874. Are the possibilities of finding the answer on the two websites independent?

• Yes, because (0.95)(0.92) = 0.874

• No, because (0.95)(0.92) = 0.874

• Yes, because 0.95 > 0.92 > 0.874

• No, because 0.5(0.95 + 0.92) ≠ 0.874

• There is insufficient information to answer this question.

Prob #3: Suppose 80% of jurors come to a just decision. In a jury of six people, what is the probability more than half come to a just decision?

• 0.09888

• 0.34464

• 0.80000

• 0.90112

• 0.98304

Prob #5: Which of the following are true statements?

1. By the Law of Large Numbers, the mean of a random variable will get closer and closer to a specific value.
2. The standard deviation of a random variable is never negative.
3. The standard deviation of a random variable is 0 only if the random variable takes a lone single value.

• 1 and 2

• 1 and 3

• 2 and 3

• 1, 2, and 3

• None of the above gives the complete set of true responses.

Prob #6: 53% of adults say they have trouble sleeping. If a doctor contacts an SRS of 85 adults, what is the probability that over 55% will say they have trouble sleeping?

• 0.3109

• 0.3558

• 0.3640

• 0.4000

• 0.6442

Prob #7: A television game show has three payoffs with the following probabilities:

Payoff $0 = Probability of 0.7

Payoff $500 = Probability of 0.25

Payoff $5000 = Probability of 0.05

What are the mean and standard deviation of the payoff variable?

• μ = 375, σ = 361

• μ = 375, σ = 1083

• μ = 1833, σ = 1816

• μ = 1833, σ = 2248

• None of the above gives a set of correct answers.

Prob #8: An insurance company charges $900 annually for auto policies for teenagers. The policy specifies the company will pay $1,500 for a minor accident and $8,000 for a major accident. If the probability of a teenager having a minor accident during the year is 0.15, and of having a major accident is 0.05, how much can the insurance company expect to make on 10 policies?

• $275

• $625

• $2,750

• $6,250

• $9,000

Prob #11: The owner of a coffee shop, an amateur statistician, advertises that the price of coffee on any given day will be randomly picked using a normal distribution with mean $1.35 and standard deviation $0.10. If a customer buys a cup of coffee on 10 days, what is the probability that he will pay a total exceeding $14.00?

• 0.0316

• 0.0568

• 0.3085

• 0.3160

• 0.9432

Prob #12: If P(A) = 0.25 and P(B) = 0.34, what is P(A U B) if A and B are independent?

• 0.085

• 0.505

• 0.590

• 0.675

• There is insufficient information to answer this question.

Prob #15: Which of the following are true statements?

1. The area under a normal curve is always equal to 1, no matter what the mean and standard deviation are.
2. The smaller the standard deviation of a normal curve, the higher and narrower the graph.
3. Normal curves with different means are centered around different numbers.

• 1 and 2

• 1 and 3

• 2 and 3

• 1, 2, and 3

• None of the above gives the complete set of true responses.

Prob #16: A piece of clothing takes an average of 38 minutes to move through an assembly line. If the standard deviation is 4 minutes, and the distribution is normal, what is the probability that a piece of clothing will take over 45 minutes?

• 0.040

• 0.080

• 0.175

• 0.227

• 0.460