Exam 7: Sampling Distributions

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

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 more than what percentage of customers who will make a purchase after visiting the web site?

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 ______.

If the expected value of a sample statistic is equal to the parameter it is estimating, then we call that sample statistic

The sample proportion is an unbiased estimator for the population proportion.

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.The expected percentage of minority students in their next group of freshmen 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 no more than $3.0 million.

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 between 14% and 24% who have high-speed access to the Internet.

The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound.If a sample of 16 fish is taken, what would the standard error of the mean weight equal?

The amount of time it takes to complete an examination has a left skewed distribution with a mean of 65 minutes and a standard deviation of 8 minutes.If 64 students were randomly sampled, the probability that the sample mean of the sampled students exceeds 71 minutes is approximately 0.

Why is the Central Limit Theorem so important to the study of 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, the standard error of all the sample proportions is ______.

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.