Why are standard z values so important? Is it true that z values have no units of measurement? Why would this be desirable for comparing data sets with different units of measurement? How can we assess differences in quality or performance by simply comparing z values under a standard normal curve? Examine the formula to compute standard z values. Notice it involves both the mean and standard deviation. Recall that in Chapter 3 we commented that the mean of a data collection was not entirely adequate to describe the data; you need the standard deviation as well. Discuss this topic again in the light of what you now know about normal distributions and standard z values.

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2) If you look up the word empirical in a dictionary, you will find that it means relying on experiment and observation rather than on theory. Discuss the empirical rule in this context. The empirical rule certainly applies to the normal distribution, but does it also apply to a wide variety of other distributions that are not exactly (theoretically) normal? Discuss the terms mound-shaped and symmetrical. Draw several sketches of distributions that are mound-shaped and symmetrical. Draw sketches of distributions that are not mound-shaped or symmetrical.To which distributions will the empirical rule apply?

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3) Consider an x distribution with standard deviation = 34.

(a) If specifications for a research project require the standard error of the corresponding x distribution to be 2, how large does the sample size need to be?

n =

(b) If specifications for a research project require the standard error of the corresponding x distribution to be 1, how large does the sample size need to be?

n =

4) Suppose the heights of 18-year-old men are approximately normally distributed, with mean 73 inches and standard deviation 3 inches.

(a) What is the probability that an 18-year-old man selected at random is between 72 and 74 inches tall? (Round your answer to four decimal places.)

(b) If a random sample of twenty-four 18-year-old men is selected, what is the probability that the mean height x is between 72 and 74 inches? (Round your answer to four decimal places.)

5) Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean = 8150 and estimated standard deviation = 2900. A test result of x < 3500 is an indication of leukopenia. This indicates bone marrow depression that may be the result of a viral infection.

(a) What is the probability that, on a single test, x is less than 3500? (Round your answer to four decimal places.)

What is the probability of x < 3500? (Round your answer to four decimal places.)

(c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)

6) Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 89 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean = 89 tons and standard deviation = 1 ton.

(a) What is the probability that one car chosen at random will have less than 88.5 tons of coal? (Round your answer to four decimal places.)

(b) What is the probability that 40 cars chosen at random will have a mean load weight x of less than 88.5 tons of coal? (Round your answer to four decimal places.)

7) What price do farmers get for their watermelon crops? In the third week of July, a random sample of 38 farming regions gave a sample mean of x = $6.88 per 100 pounds of watermelon. Assume that is known to be $1.90 per 100 pounds.

(a) Find a 90% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop. What is the margin of error? (Round your answers to two decimal places.)

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(b) Find the sample size necessary for a 90% confidence level with maximal error of estimate E = 0.31 for the mean price per 100 pounds of watermelon. (Round up to the nearest whole number.)

farming regions

(c) A farm brings 15 tons of watermelon to market. Find a 90% confidence interval for the population mean cash value of this crop. What is the margin of error? Hint: 1 ton is 2000 pounds. (Round your answers to two decimal places.)

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8) Twenty-eight small communities in Connecticut (population near 10,000 each) gave an average of x = 138.5 reported cases of larceny per year. Assume that is known to be 42.7 cases per year.

(a) Find a 90% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

lower limit

upper limit

margin of error

(b) Find a 95% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

lower limit

upper limit

margin of error

(c) Find a 99% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error? (Round your answers to one decimal place.)

lower limit

upper limit

margin of error