Exam 7: Sampling Distributions

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. So, the middle 95% of the sample means based on samples of size 36 will be between __________ and __________.

SCENARIO 7-5 According to an article, 19% of the entire population in a developing country have 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 14% and 24% who have high-speed access to the Internet.

The standard error of the mean

A sampling distribution is a distribution for a statistic.

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, the mean of all the sample proportions of customers who will make a purchase after visiting the web site is _______.

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 was less than $2.5 million.

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 of online customer service.

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. So, the mally distributed with iddle 70% of all sample means will fall between what two values?

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, the standard deviation of all the sample proportions of U.S. consumers who will spend more on holiday shopping is ________.

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 was no more than $3.0 million.

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, the mean of all the sample proportions of Chinese consumers who will spend more on holiday shopping is _______.

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, the requirements for using a normal distribution to approximate a binomial distribution is fulfilled for the random samples of Canadian consumers.

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 between $820 and $840?

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.

Suppose μ = 50 and σ = 10 for a population. In a sample where n = 100 is randomly taken, 95% of all possible sample means will fall between 48.04 and 51.96.

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 less than 900 hours?

The standard error of the mean is also known as the standard deviation of the sampling distribution of the sample mean.

The mean score of all pro golfers for a particular course has a mean of 70 and a standard deviation of 3.0. Suppose 36 pro golfers played the course today. Find the probability that the mean score of the 36 pro golfers exceeded 71.

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, the requirements for using a normal distribution to approximate a binomial distribution is fulfilled for the random samples of U.S. consumers.