Exam 7: Sampling and Sampling Distributions

According to the Bureau of Labor Statistics it takes an average of 22 weeks for someone over 55 to find a new job.Assume that the probability distribution is normal and that the standard deviation is two weeks.What is the probability that eight workers over the age of 55 take an average of more than 20 weeks to find a job?

Suppose residents in a well-to-do neighborhood pay an average overall tax rate of 25% with a standard deviation of 8%.Assume tax rates are normally distributed.What is the probability that the mean tax rate of 16 randomly selected residents is between 20% and 30%?

Suppose the average casino patron in Las Vegas loses $110 per day,with a standard deviation of $700.Assume winnings/losses are normally distributed.a.What is the probability that a random group of nine people averages more than $500 in winnings on their one-day trip to Las Vegas? b.What is the probability that a random group of nine people averages more than $500 in losses on their one-day trip to Las Vegas?

Susan has been on a bowling team for 14 years.After examining all of her scores over that period of time,she finds that they follow a normal distribution.Her average score is 225,with a standard deviation of 13.If during a typical week Susan bowls 16 games,what is the probability that her average score is more than 230?

The central limit theorem approximation improves as the sample size decreases.

For quantitative data,the most appropriate control chart to monitor central tendency is a(n)

In a recent investigation,the National Highway Traffic Safety Administration (NHTSA)found that the Chevrolet Volt and other electric vehicles do not pose a greater risk of fire than gasoline-powered vehicles (The Boston Globe,January 25,2012).Specifically,it was determined that "no discernible defect trend exists." Suppose a consumer advocacy group wants to verify some of these claims by constructing a chart.The group expects 2% of electric cars to catch fire each month.For each of the last six months,500 electric car owners are asked if their cars have caught fire.These sample proportions are obtained: 0.010 0.020 0.015 0.030 0.025 0.015.a.Assuming that the group expectation is correct,construct the centerline and the upper and lower control limits for the chart.b.Do the consumer group's findings support those of the NHTSA? Explain the answer.

Which of the following is true about statistics such as the sample mean or sample proportion?

A gym knows that each member,on average,spends 70 minutes at the gym per week,with a standard deviation of 20 minutes.Assume the amount of time each customer spends at the gym is normally distributed.a.What is the probability that a randomly selected customer spends less than 65 minutes at the gym? b.Suppose the gym surveys a random sample of 49 members about the amount of time they spend at the gym each week.What are the expected value and standard deviation (standard error)of the sample mean of the time spent at the gym? c.If 49 members are randomly selected,what is the probability that the average time spent at the gym exceeds 75 minutes?

The standard deviation of suggests that the variation between observations is smaller than the variation between averages.

For any population X with expected value µ and standard deviation σ,the sampling distribution of will be approximately normal if the sample size n is sufficiently small.As a general guideline,the normal distribution approximation is justified when n < 30.

A random sample of size 100 is taken from a population described by the proportion p = 0.60.The probability that the sample proportion is less than 0.55 is _______.

If a population is known to be normally distributed,what can be said of the sampling distribution of the sample mean drawn from this population?

A random sample of size 100 is taken from a population described by the proportion p = 0.60.The probability that the sample proportion is greater than 0.62 is _______.

Susan has been on a bowling team for 14 years.After examining all of her scores over that period of time,she finds that they follow a normal distribution.Her average score is 225,with a standard deviation of 13.If during a typical week Susan bowls 16 games,what is the probability that her average score for the week is between 220 and 228?

Susan has been on a bowling team for 14 years.After examining all of her scores over that period of time,she finds that they follow a normal distribution.Her average score is 225,with a standard deviation of 13.What is the probability that in a one-game playoff,her score is more than 227?

The labor force participation rate is the number of people in the labor force divided by the number of people in the country who are of working age and not institutionalized.The BLS reported in February 2012 that the labor force participation rate in the United States was 63.7% (Calculatedrisk.com).A marketing company asks 120 working-age people if they either have a job or are looking for a job,or,in other words,whether they are in the labor force.For the company's sample,the probability that the proportion of people who are in the labor force is greater than 0.65 is _______.

Professor Elderman has given the same multiple-choice final exam in his Principles of Microeconomics class for many years.After examining his records from the past 10 years,he finds that the scores have a mean of 76 and a standard deviation of 12.What is the probability Professor Elderman's class of 36 has a class average below 78?

A random sample of size 100 is taken from a population described by the proportion p = 0.60.The probability that the sample proportion is between 0.55 and 0.62 is _______.

Suppose that,on average,electricians earn approximately µ = $54,000 per year in the United States.Assume that the distribution for electricians' yearly earnings is normally distributed and that the standard deviation is σ = $12,000.What is the probability that the average salary of four randomly selected electricians is less than $50,000?