Exam 7: Sampling Distributions

SCENARIO 7-5 According to an article, 19% of the entire population in a developing country has high-speed access to the Internet.Random samples of size 200 are selected from the country's population. -Referring to Scenario 7-5, among all the random samples of size 200, % will have between 9% and 29% who have high-speed access to the Internet.

A manufacturer of power tools claims that the mean amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes.Suppose arandom sample of 64 purchasers of this table saw is taken.The standard deviation of the samplingdistribution of the sample mean is minutes.

SCENARIO 7-2 The mean selling price of new homes in a small town over a year was $115,000.The population standard deviation was $25,000.A random sample of 100 new home sales from this city was taken. -Referring to Scenario 7-2, what is the probability that the sample mean selling price was between$114,000 and $116,000?

For sample sizes greater than 30, the sampling distribution of the mean will be approximately normally distributed

At a computer manufacturing company, the actual size of a computer chip is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter.A random sample of 12 computer chips is taken.Above what value do 2.5% of the sample means fall?

The amount of tea leaves in a can from a production line is normally distributed with $\mu = 110$ grams and $\sigma = 25$ grams.A sample of 25 cans is to be selected.What is the probability that thesample mean will be between 100 and 120 grams?

The distribution of the number of loaves of bread sold per week by a large bakery over the past 5 years has a mean of 7,750 and a standard deviation of 145 loaves.Suppose a random sample ofn = 40 weeks has been selected.What is the approximate probability that the mean number ofloaves sold in the sampled weeks exceeds 7,895 loaves?

The sample mean is an unbiased estimator for the population mean.

SCENARIO 7-4 According to a survey, only 15% of customers who visited the web site of a major retail store made a purchase.Random samples of size 50 are selected. -Referring to Scenario 7-4, what proportion of the samples will have less than 15% of customers who will make a purchase after visiting the web site?

The sample mean is an unbiased estimate of the population mean.

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past.Suppose a sample of 100 major league players was taken.Find the approximate probability that the mean salary of the 100 players exceeded $4.0 million.

At a computer manufacturing company, the actual size of a computer chip is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter.A random sample of 12 computer chips is taken.What is the standard error for the sample mean?

SCENARIO 7-4 According to a survey, only 15% of customers who visited the web site of a major retail store made a purchase.Random samples of size 50 are selected. -Referring to Scenario 7-4, 90% of the samples will have more than what percentage of customers who will make a purchase after visiting the web site?

The amount of bleach a machine pours into bottles has a mean of 36 oz.with a standard deviation of 0.15 oz.Suppose we take a random sample of 36 bottles filled by this machine.The sampling distribution of the sample mean has a mean of 36 oz.

SCENARIO 7-6 Online customer service is a key element to successful online retailing.According to a marketing survey, 37.5% of online customers take advantage of the online customer service.Random samples of 200 customers are selected. -Referring to Scenario 7-6, % of the samples are likely to have between 35% and 40% who take advantage of online customer service.

SCENARIO 7-1 The time spent studying by students in the week before final exams follows a normal distribution with a standard deviation of 8 hours.A random sample of 4 students was taken to estimate the mean study time for the population of all students. -Referring to Scenario 7-1, what is the probability that the sample mean is more than 3 hours below the population mean?

SCENARIO 7-6 Online customer service is a key element to successful online retailing.According to a marketing survey, 37.5% of online customers take advantage of the online customer service.Random samples of 200 customers are selected. -Referring to Scenario 7-6, 90% of the samples proportions symmetrically around the population proportion will have between _% and _% of the customers who take advantage ofonline customer service.

The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound.If a sample of25 fish yields a mean of 3.6 pounds, what is the Z-score for this observation?

The fact that the sample means are less variable than the population data can be observed from the standard error of the mean.

SCENARIO 7-6 Online customer service is a key element to successful online retailing.According to a marketing survey, 37.5% of online customers take advantage of the online customer service.Random samples of 200 customers are selected. -Referring to Scenario 7-6, % of the samples are likely to have less than 37.5% who take advantage of online customer service.