Exam 7: Sampling Distributions

SCENARIO 7-3 The lifetimes of a certain brand of light bulbs are known to be normally distributed with a mean of 1,600 hours and a standard deviation of 400 hours.A random sample of 64 of these light bulbs is taken. -Referring to Scenario 7-3, the probability is 0.20 that the sample mean lifetime differs from the population mean lifetime by at least how many hours?

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 probability that the mean of the sample exceeds 36.01 oz.is __________.

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.

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.

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, what is the probability less than 23% of the entire population will have high-speed access to the Internet?

If the amount of gasoline purchased per car at a large service station has a population mean of 15 gallons and a population standard deviation of 4 gallons and a random sample of 4 cars is selected, there is approximately a 68.26% chance that the sample mean will be between 13 and 17 gallons.

True or False When working with a very large (or "infinite")population or a population sampled with replacement, the finite population correction (fpc)is used in computing the standard error.

A written survey is conducted at a college where the administration wants to estimate the number of students wishing to form a student union.There are 7,000 students on campus. In a simple random sample of 600, 420 were in favor of establishing a student union. Compute the standard error )of the proportion

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 probability that the sample mean will be between 77 and 89 minutes is __________.

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, what is the probability more than 16% of the entire population will 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 a random sample of 64 purchasers of this table saw is taken.The probability that the sample mean will be greater than 88 minutes is __________.

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?

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 less than what percentage 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 more than half of the students in the sample will be minority students.

The standard error of the mean for a sample of 100 is 30.To cut the standard error of the mean to 15, we would

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, without doing the calculations, state in which of the following ranges the sample mean selling price is most likely to lie?

Suppose a sample of n = 50 items is selected from a population of manufactured products and the weight, X, of each item is recorded.Prior experience has shown that the weight has a probability distribution with ounces and ounces.Which of the following is true about the sampling distribution of the sample mean if a sample of size 15 is selected?

The amount of tea leaves in a can from a production line is normally distributed with grams and grams.A sample of 25 cans is to be selected.So, 95% of all sample means will be greater than how many grams?

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?

The Central Limit Theorem is important in statistics because