Exam 7: Sampling Distributions

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, 90 % will have more than _____% who have high-speed access to the Internet.

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 probabilityally distributed with that the sample mean will be greater than 100 grams?

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 μ = 6 ounces and σ = 2.5 ounces. Which of the following is true about the Sampling distribution of the sample mean if a sample of size 15 is selected?

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 U.S. consumers will have at least 45% of consumers who will spend more on holiday shopping?

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. Above what value do 2.5% of the sample means fall?

Which of the following is true about the sampling distribution of the sample mean?

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?

A sampling distribution is defined as the probability distribution of possible sample sizes that can be observed from a given population.

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 Canadian consumers will have at least 45% 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 standard error of all possible sample proportions is ______.

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 between 35.95 and 35.98 oz. is __________.

Suppose μ = 80 and σ = 20 for a population. In a sample where n = 100 is randomly taken, 95% of all possible sample means will fall above 76.71.

An unbiased estimator will have a value, on average across samples, equal to the population parameter value.

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.

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?

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?

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

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 less than 20% who have high-speed access to the Internet.

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, what is the probability that the sample mean lifetime is more than 1,550 hours?

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?