Exam 7: Sampling Distributions

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, among all the random samples of size 200, 90 % will have less than% that has high-speed access to the Internet.

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 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 will be approximately normal only if the population sampled is normal.

To use the normal distribution to approximate the binomial distribution, we need andto be at least 5.

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 7-2 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 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 standard error of 0.15.

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.

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.What was the standard error for the sample mean salary?

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 .

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, among all the random samples of size 200, % will have less than 20% who have high-speed access to the Internet.

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, among all the random samples of size 200, 90 % will have more than% who have high-speed access to the Internet.

Suppose the ages of students in Statistics 101 follow a right skewed distribution with a mean of23 years and a standard deviation of 3 years.If we randomly sampled 100 students, which of the following statements about the sampling distribution of the sample mean age is incorrect?

Sampling distributions describe the distribution of

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.

The Central Limit Theorem is important in statistics because

A study at a college in the west coast reveals that, historically, 45% of the students are minority students.If random samples of size 75 are selected, 80% of the samples will have less than% of minority students.

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 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.

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