Exam 7: Sampling Distributions

Sales prices of baseball cards from the 1960s are known to possess a right skewed distribution with a mean sale price of $5.25 and a standard deviation of $2.80.Suppose a random sample of 100 cards from the 1960s is selected.Describe the sampling distribution for the sample mean sale price of the selected cards.

If the population distribution is skewed,in most cases the sampling distribution of the mean can be approximated by the normal distribution if the samples contain at least 30 observations.

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 a random sample of 64 purchasers of this table saw is taken.The standard deviation of the sampling distribution of the sample mean is _____ minutes.

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?

A sample of size 25 provides a sample variance of 400.The standard error,in this case equal to 4,is best described as the estimate of the standard deviation of means calculated from samples of size 25.

As the size of the sample is increased,the standard deviation of the sampling distribution of the sample mean for a normally distributed population will stay the same.

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 a random sample of 64 purchasers of this table saw is taken.The mean of the sampling distribution of the sample mean is _____ minutes.

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 is the probability that a random sample of 50 will have at least 30% of customers who will make a purchase after visiting the web site?

For distributions such as the normal distribution,the arithmetic mean is considered more stable from sample to sample than other measures of central tendency.

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

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.What percentage of samples of 4 fish will have sample means between 3.0 and 4.0 pounds?

The Central Limit Theorem ensures that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases.

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 $3.5 million.

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 of n = 40 weeks has been selected.What is the approximate probability that the mean number of loaves sold in the sampled weeks exceeds 7,895 loaves?

For sample size 16,the sampling distribution of the mean will be approximately normally distributed

The amount of tea leaves in a can from a production line is normally distributed with μ = 110 grams and σ = 25 grams.A sample of 25 cans is to be selected.What is the probability that the sample mean will be greater than 100 grams?

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 more than $110,000?

The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes.A random sample of 16 cars is selected.What is the probability that the sample mean will be between 39 and 48 minutes?

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 between 20% and 30% of customers who will make a purchase after visiting the web site?

A study at a college in the west coast reveals that,historically,45% of the students are minority students.If a random sample of size 75 is selected,the probability is_____ that between 30% and 50% of the students in the sample will be minority students.