Probability Distributions

The lifetime of a particular type of car tire is normally distributed. The mean lifetime is 50,000 miles, with a standard deviation of 5,000 miles. Of a random sample of 15,000 tires, how many of the tires are expected to last for between 45,000 and 55,000 miles?

• 7,125

• 10,200

• 14,250

• 14,850

If the Stanford IQ test is a normal curve with mean of 100 and standard deviation of 20, what percent of the population has an IQ below 90?

• 41.73%

• 12.15%

• 88.87%

• 30.85%

• 1375

• 2750

• 8500

• 2375

A new drug cures 75% of the patients who take it. If it is given to 16 patients, what is the probability that at least 11 will be cured?

• .18

• .36

• .63

• .83

• I only

• ! and III only

• I and II only

• II and III only

In a multiple-choice test each question has five possible answers. Five points are given for each correct answer but one point is deducted for each incorrect answer. What is the expected value for a question that is answered by randomly guessing the answer?

• 0.2

• -0.2

• 0

• 0.4

A company that manufactures tires produces a tire that has an average life span of 65,000 kilometers with a standard deviation of 5,200 kilometers. The distribution of the life spans of the tire is normal. What percent of the tires last at least 61,000 kilometers?

• 98.2%

• 82.3%

• 77.9%

• 74.7%

A hockey goaltender has a save percentage of 0.920. This means that the probability of any single shot taken on the goaltender being a goal is 0.08%. What would be the expected number of goals scored on the goaltender in a game where she faced 43 shots?

• 2.6

• 2.8

• 3.2

• 3.44

Suppose the warranty period on your family's new television is about to expire and you are debating about whether to buy a one-year maintenance contract for $35. If you buy the contract, all repairs for one year are free. Consumer information shows that 14% of the TV's like yours require an annual repair that cost $150 on the average. What is the expected value of buying the maintenance contract?

• -14

• -18.5

• -6

• 2

• 1.7

• 2.0

• 2.1

• 1.6