Assume that the sample is taken from a large

Problem 1E If samples of a specific size are selected from a population and the means are computed, what is this distribution of means called?

Problem 2E Why do most of the sample means differ somewhat from the population mean? What is this difference called?

Problem 3E What is the mean of the sample means?

Problem 5E What does the central limit theorem say about the shape of the distribution of sample means?

What is the standard deviation of the sample means called? What is the formula for this standard deviation?

Problem 8E Assume that the sample is taken from a large population and the eorrection factor can be ignored. Class Garbage GenerationA survey found that the American family generates an average of 17.2 pounds of glass garbage each year. Assume the standard deviation of the distribution is 2.5 pounds, find the probability that the mean of a sample of 55 families will be between 17 and 18 pounds.

What formula is used to gain information about an individual data value when the variable is normally distributed?

Problem 9E Assume that the sample is taken from a large population and the eorrection factor can be ignored. College CostsThe mean undergraduate cost for tuition, fees. room, and board for four-year institutions was $26,489 for a recent academic year. Suppose that ? = $3204 and that 36 four-year institutions are randomly selected. Find the probability that the sample mean cost for these 36 schools is a. Less than $25.000 ________________ b. Greater than $26,000 ________________ c. Between $24,000 and $26,000

Problem 14E Assume that the sample is taken from a large population and the eorrection factor can be ignored. SAT ScoresThe national average SAT score (for Verbal and Math) is 1028. Suppose that nothing is known about the shape of the distribution and that the standard deviation is 100. If a random sample of 200 scores were selected and the sample mean were calculated to be 1050, would you be surprised? Explain.

Problem 16E Assume that the sample is taken from a large population and the eorrection factor can be ignored. Cell Phone LifetimesA recent study of the lifetimes of cell phones found the average is 24.3 months. The standard deviation is 2.6 months. If a company provides its 33 employees with a cell phone, find the probability that the mean lifetime of these phones will be less than 23.8 months. Assume cell phone life is a normally distributed variable.

Problem 10E Assume that the sample is taken from a large population and the eorrection factor can be ignored. Teachers’ Salaries in ConnecticutThe average teacher’s salary in Connecticut (ranked first among states) is $57,337. Suppose that the distribution of salaries is normal with a standard deviation of $7500. a. What is the probability that a randomly selected teacher makes less than $52.000 per year? ________________ b.If we sample 100 teachers’ salaries, what is the probability that the sample mean is less than 556,000?

Problem 11E Assume that the sample is taken from a large population and the eorrection factor can be ignored. Serum Cholesterol LevelsThe mean serum cholesterol level of a large population of overweight children is 220 milligrams per deciliter (mg/dl), and the standard deviation is 16.3 mg/dl. If a random sample of 35 overweight children is selected, find the probability that the mean will be between 220 and 222 mg/dl. Assume the serum cholesterol level variable is normally distributed.

Problem 12E Assume that the sample is taken from a large population and the eorrection factor can be ignored. Teachers’Salaries in North DakotaThe average teacher’s salary in North Dakota is $37,764. Assume a normal distribution with ? = $5100. a. What is the probability that a randomly selected teacher’s salary is greater than $45,000? ________________ b. For a sample of 75 teachers, what is the probability that the sample mean is greater than $38.000?

Assume that the sample is taken from a large population and the eorrection factor can be ignored. Per Capita Income of Delaware ResidentsIn a recent year. Delaware had the highest per capita annual income with $51.803. If ? = $4850. what is the probability that a random sample of 34 state residents had a mean income greater than $50,000? Less than $48,000?

Problem 17E Assume that the sample is taken from a large population and the eorrection factor can be ignored. Water UseThe Old Farmer’s Almanac reports that the average person uses 123 gallons of water daily. If the standard deviation is 21 gallons, find the probability that the mean of a randomly selected sample of 15 people will be between 120 and 126 gallons. Assume the variable is normally distributed.

Problem 18E Assume that the sample is taken from a large population and the eorrection factor can be ignored. Medicare Hospital InsuranceThe average yearly Medicare Hospital Insurance benefit per person was $4064 in a recent year. If the benefits are normally distributed with a standard deviation of $460. find the probability that the mean benefit for a random sample of 20 patients is a. Less than $3800 ________________ b. More than $4100

Problem 19E Assume that the sample is taken from a large population and the eorrection factor can be ignored. Amount of Laundry Washed Each YearProcter & Gamble reported that an American family of four washes an average of 1 ton (2000 pounds) of clothes each year. If the standard deviation of the distribution is 187.5 pounds, find the probability that the mean of a randomly selected sample of 50 families of four will be between 1980 and 1990 pounds.

Problem 21E Assume that the sample is taken from a large population and the eorrection factor can be ignored. Annual PrecipitationThe average annual precipitation for a large Midwest city is 30.85 inches with a standard deviation of 3.6 inches. Assume the variable is normally distributed. a. Find the probability that a randomly selected month will have less than 30 inches. ________________ b. Find the probability that the mean of a random selection of 32 months will have a mean less than 30 inches. ________________ c. Does it seem reasonable that one month could have a rainfall amount less than 30 inches? ________________ d. Does it seem reasonable that the mean of a sample of 32 months could be less than 30 inches?

Problem 22E Assume that the sample is taken from a large population and the eorrection factor can be ignored. Systolic Blood Pressure Assume that the mean systolic blood pressure of normal adults is 120 millimeters of mercury (mm Hg) and the standard deviation is 5.6. Assume the variable is normally distributed. a. If an individual is selected, find the probability that the individual’s pressure will be between 120 and 121.8 mm Hg. ________________ b. If a sample of 30 adults is randomly selected, find the probability that the sample mean will be between 120 and 121.8 mm Hg. ________________ c. Why is the answer to part a so much smaller than the answer to part b?

Assume that the sample is taken from a large population and the correction factor can be ignored. Cholesterol ContentThe average cholesterol content of a certain brand of eggs is 215 milligrams, and the standard deviation is 15 milligrams. Assume the variable is normally distributed. a. If a single egg is selected, find the probability that the cholesterol content will be greater than 220 milligrams. b. If a sample of 25 eggs is selected, find the probability that the mean of the sample will be larger than 220 milligrams.

The standard deviation of a variable is 15. If a sample of 100 individuals is selected, compute the standard error of the mean. What size sample is necessary to double the standard error of the mean?

Check to see whether the correction factor should be used. If so, be sure to include it in the calculations Home ValuesA study of 800 homeowners in a certain area showed that the average value of the homes was $82.000, and the standard deviation was $5000. If 50 homes are for sale, find the probability that the mean of the values of these homes is greater than $83.500.

In Exercise 29, what size sample is needed to cut the standard error of the mean in half?

For Exercises 7 through 25, assume that the sample is taken from a large population and the correction factor can be ignored. Ages of Proofreaders At a large publishing company, the mean age of proofreaders is 36.2 years, and the standard deviation is 3.7 years. Assume the variable is normally distributed. a. If a proofreader from the company is randomly selected, find the probability that his or her age will be between 36 and 37.5 years. b. If a random sample of 15 proofreaders is selected, find the probability that the mean age of the proofreaders in the sample will be between 36 and 37.5 years.

Problem 28EC Breaking Strength of Steel Cable The average breaking strength of a certain brand of steel cable is 2000 pounds, with a standard deviation of 100 pounds. A sample of 20 cables is selected and tested. Find the sample mean that will cut off the upper 95% of all samples of size 20 taken from the population. Assume the variable is normally distributed.

For Exercises 26 and 27, check to see whether the correction factor should be used. If so, be sure to include it in the calculations. Life Expectancies In a study of the life expectancy of 500 people in a certain geographic region, the mean age at death was 72.0 years, and the standard deviation was 5.3 years. If a sample of 50 people from this region is selected, find the probability that the mean life expectancy will be less than 70 years.