1. State Sales Tax. 2. Baggage Check

Transcription

1 1. State Sales Tax A survey asks a random sample of 1500 adults in Ohio if they support an increase in the state sales tax from 5% to 6% with the additional revenue going to education. If 40% of all adults in Ohio support the increase, how large of a sample would be needed to guarantee the standard deviation of ô is no more than 0.01? 2. Baggage Check Think back to the green light baggage check example. Customs agents said the probability the light shows green is 0.7 on each press of the button. You observe 100 passengers and only 65 get a green light. a.) Doe this give you reason to doubt the customs officials? b.) Describe the sampling distribution for n= 100 passengers. 1

2 3. Women and Time If 47% of all women don t think they get enough time for themselves and an opinion poll interviews 102 randomly chosen women and records the sample proportion who feel they don t get enough time for themselves. a.) Describe the sampling distribution of ô. b.) If p = 0.47, in what range will the middle 95% of all sample results fall? c.) What is the probability the poll gets a sample in which fewer than 45% say they don t get enough time for themselves? 4. Fire Insurance An insurance company sees that in the entire population of homeowners, the mean loss from fire is μ = $250 and the standard deviation of the loss is σ = $300. The distribution is strongly skewed right. If the company sells 10,000 policies, what is the approximate probability the average loss will be greater than $260? 2

3 5. Rush Hour Traffic A study of rush hour traffic in San Francisco counts the number of people in each car entering a freeway at a suburban interchange. Suppose this count has mean 1.5 and standard deviation 0.75 in the population of all cars that enter the interchange during rush hour. a.) Could the exact distribution of the count be normal? Why or why not? b.) Traffic engineers estimate the capacity of the interchange to be 700 cars per hour. According to the Central Limit Theorem, what is the approximate distribution of the mean number of people x in 700 randomly selected cars? c.) What is the probability that 700 cars will carry more than 1075 people? 6. Jogging Suppose that 15% of adults jog. Find the probability that an SRS of 200 people measures ô within 2 percentage points. What if the SRS were of 3200 people? 3

4 7. Power Companies Power companies kill trees growing near their lines to avoid power failures due to falling limbs in storms. Applying a chemical to slow the growth of the trees is cheaper than trimming, but the chemical kills some of the trees. Suppose that one such chemical would kill 20% of sycamore trees. The power company tests the chemical on 250 sycamores. Consider these an SRS from the population of all sycamore trees. a.) What are the mean and standard deviation of the proportion of trees that are killed? b.) What is the probability that at least 60 trees (24% of the sample) are killed? 8. Parameter or Statistic? Are the underlined numbers parameters or statistics? Use appropriate notation to describe each number. A random sample of male college students has a mean height of 66.5 which is greater than the 64 mean height of all American men. 4

5 9. Soda Bottles A bottling company uses a filling machine to fill plastic bottle with soda. The bottles are supposed to contain 300 ml. In fact, the contents vary according to a normal distribution with mu = 298ml and sigma = 3 ml. a.) What is the probability an individual bottle contains less than 295 ml? b.) What is the probability the mean contents of 6 randomly selected bottles is less than 295 ml? 10. Rules of thumb Why can t you use the rules of thumb in these situations? a.) A factory employs 3000 unionized workers of whom 30% are Spanish. The 15 member union executive committee contains 3 Hispanics. What would the probability be of 3 or fewer Hispanics if the executive committee were chosen at random from all of the workers? b.) A university study committee chooses an SRS of 50 of the 316 athletes to interview about academics. If 40% of athletes have been told by their coach to neglect their studies on at least one occasion, what is the probability that at least 15 in the sample are among this group? 5

6 Answers a) Not really, it would happen with probability b) N(0.7, ) 3. a) N(0.47, 0.049) b) c) p = (very small) 5. a) no b) (1.5, 0.028) c) a) 57.17% b) a) (0.2, 0.025) b) p = Parameter: 64; statistic: a) b) a) Np is not >10 b) pop not 10x sample 6