Exam 7: Sampling Distributions

At a computer manufacturing company, the actual size of a particular type of computer chips 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 probability that the sample mean will be between 0.99 and 1.01 centimeters?

As the sample size increases, the standard error of the mean increases.

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 is between 45 and 52 minutes?

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 is less than 36.03 is __________.

For air travelers, one of the biggest complaints is of the waiting time between when the airplane taxis away from the terminal until the flight takes off. This waiting time is known to have a right Skewed distribution with a mean of 10 minutes and a standard deviation of 8 minutes. Suppose 100 flights have been randomly sampled. Describe the sampling distribution of the mean waiting Time between when the airplane taxis away from the terminal until the flight takes off for these 100 flights.

SCENARIO 7-8 A consulting firm that surveyed consumers' holiday shopping behavior found that the percentage of consumers from the U.S., Canada, and China who said that they planned to spend more on holiday shopping were 40%, 34% and 73%, respectively. Treat these results as representations of the populations. Random samples of size 150 are selected from each of the three countries. -Referring to Scenario 7-8, 90% of the samples from China will have more than what percentage of consumers who will spend more on holiday shopping?

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 7-8 A consulting firm that surveyed consumers' holiday shopping behavior found that the percentage of consumers from the U.S., Canada, and China who said that they planned to spend more on holiday shopping were 40%, 34% and 73%, respectively. Treat these results as representations of the populations. Random samples of size 150 are selected from each of the three countries. -Referring to Scenario 7-8, what is the probability that a random sample of 150 Chinese consumers will have at least 45% of consumers who will spend more on holiday shopping?

μThe am = 110 gramount of tea leaves in a can froms and σ = 25 grams. A sam a particular production line is normple of 25 cans is to be selected. What is the ally distributed with probability that the sample mean will be less than 100 grams?

SCENARIO 7-8 A consulting firm that surveyed consumers' holiday shopping behavior found that the percentage of consumers from the U.S., Canada, and China who said that they planned to spend more on holiday shopping were 40%, 34% and 73%, respectively. Treat these results as representations of the populations. Random samples of size 150 are selected from each of the three countries. -Referring to Scenario 7-8, what proportion of the samples from China will have between 30% and 50% of consumers who will spend more on holiday shopping?

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, the population mean of all possible sample proportions is ______.

Which of the following is true regarding the sampling distribution of the mean for a large sample size?

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 0.15 that the sample mean lifetime is more than how many hours?

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.

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?

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

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

SCENARIO 7-7 A recent survey revealed that American's Christmas spending averaged $830. Use this as the population mean American's Christmas spending. Suppose American's Christmas spending is normally distributed with a standard deviation of $220. Random sample of size 100 are selected from the population of American consumers. -Referring to Scenario 7-7, what is the probability that the sample mean spending is at least $800?

The Central Limit Theorem is important in statistics because

SCENARIO 7-8 A consulting firm that surveyed consumers' holiday shopping behavior found that the percentage of consumers from the U.S., Canada, and China who said that they planned to spend more on holiday shopping were 40%, 34% and 73%, respectively. Treat these results as representations of the populations. Random samples of size 150 are selected from each of the three countries. -Referring to Scenario 7-8, what proportion of the samples from Canada will have less than 35% of consumers who will spend more on holiday shopping?