2. The Medassist Pharmaceutical Company receives large ships of aspirin tablets and uses this acceptance sampling plan: Randomly select and test 24 tablets, then accept the whole batch if there is at most one aspirin that doesn't meet the required specifications. If a particular shipment of thousands of aspirin tablets actually has a 4% rate of defects, what is the probability that this whole shipment will be accepted?

When functioning correctly, a machine produces switches with a 0.8% defective rate. Find the probability that a batch of 1,000 switches contains 14 or more defective switches (assuming that the machine functions correctly, i.e., the population defective rate is 0.8%). Suppose a batch of 1,000 switches were inspected when completed, and 14 defective switches were found. Based on your answer to part a, does this sample imply that the machine needs adjustment? Explain your answer.

2. Imagine two houses that are infested with house mice. In House 1, the mice have a frequency of the "curly coat allele" of 0.7. In House 2, the frequency of that allele is 0.4. Each house contains a population of 40 mice. There are regularly 5 migrants from each house to the other every generation. а. What is m for House 1? b. What will the expected frequency of the curly coat allele be in the next generation of House 2? Show your work to the nearest 0.01. С. Is evolution occurring in these populations? How do you know?

Much is made of the fact that certain mutual funds outperform the market year after year (that is, the return from holding shares in the mutual fund is higher than the return from holding a portfolio such as the S&P 500). For concreteness, consider a 10-year period and let the population be the 4,170 mutual funds reported in The Wall Street Journal on January 1, 1995. By saying that performance relative to the market is random, we mean that each fund has a 50–50 chance of outperforming the market in any year and that performance is independent from year to year. (i) If performance relative to the market is truly random, what is the probability that any particular fund outperforms the market in all 10 years? (ii) Of the 4,170 mutual funds, what is the expected number of funds that will outperform the market in all 10 years? (iii) Find the probability that at least one fund out of 4,170 funds outperforms the market in all 10 years. What do you make of your answer? (iv) If you have a…

According to the 2000 U.S. Census Bureau, in 2000, 9.5 percent of children in the state of Ohio were not covered by private or government health insurance. In the neighboring state of Pennsylvania, 4.9 percent of children were not covered by health insurance. Assume that these proportions are parameters for the child populations of the respective states. If a random sample of size 100 children is drawn from the Ohio population, and an independent random sample of size 120 is drawn from the Pennsylvania population, what is the probability that the samples would yield a difference, ^p1 - ^p2 of .09 or more?

A pharmaceutical company receives large shipments of ibuprofen tablets and uses sampling plan to accept the shipmemts. They randomly select and test 27 tablets, and accept the entire batch if there is at most one tablet that does not meet the required specifications.Suppose a particular shipment of ibuprofen tablets has a 4% rate of defects. What is the probability that this whole shipment will be accepted?

The United States Bureau of Labor Statistics (BLS) conducts the Quarterly Census of Employment and Wages (QCEW) and reports a variety of information on each county in America. In the third quarter of 2016, the QCEW reported the total taxable earnings, in millions, of all wage earners in all 3222 counties in America. Suppose that James is an economist who collects a simple random sample of the total taxable earnings of workers in 56 American counties during the third quarter of 2016. According to the QCEW, the true population mean and standard deviation of taxable earnings, in millions of dollars, by county are ?=28.29 and ?=33.493 , respectively. Let ? be the total taxable earnings, in millions, of all wage earners in a county. The mean total taxable earnings of all wage earners in a county across all the counties in James' sample is ?⎯⎯⎯ . Use the central limit theorem (CLT) to determine the probability ? that the mean taxable wages in James' sample of 56 counties will be less than…