Exam 7: Sampling Distributions

Suppose $\mu$ = 50 and $\sigma$ = 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.

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 middle95% of the sample means based on samples of size 36 will be between and.

Assume that house prices in a neighborhood are normally distributed with a standard deviation of$20,000.A random sample of 16 observations is taken.What is the probability that the sample mean differs from the population mean by more than $5,000?

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, 95% of the samples will have more than% of minority students.

Suppose $\mu$ = 50 and $\sigma$ = 10 for a population.In a sample where n = 100 is randomly taken, 90% of all possible sample means will fall between 49 and 51.

If the amount of gasoline purchased per car at a large service station has a population mean of 15 gallons and a population standard deviation of 4 gallons and a random sample of 64 cars is selected, there is approximately a 95.44% chance that the sample mean will be between 14 and 16 gallons.

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 proportion of the samples will have between 20% and 30% of customers who will make a purchase after visiting the web site?

A sampling distribution is a distribution for a statistic.

Suppose $\mu$ = 80 and $\sigma$ = 20 for a population.In a sample where n = 100 is randomly taken, 95% of all possible sample means will fall above 76.08.

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.

At a computer manufacturing company, the actual size of a computer chip 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 below 0.95 centimeters?

The standard error of the mean for a sample of 100 is 30.To cut the standard error of the mean to15, we would

SCENARIO 7-1 The time spent studying by students in the week before final exams follows a normal distribution with a standard deviation of 8 hours.A random sample of 4 students was taken to estimate the mean study time for the population of all students. -Referring to Scenario 7-1, what is the probability that the sample mean exceeds the population mean by more than 2 hours?

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?

At a computer manufacturing company, the actual size of a computer chip 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 standard error for the sample mean?

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

As the size of the sample is increased, the standard deviation of the sampling distribution of the sample mean for a normally distributed population will stay the same.

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?

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 probability that the sample mean will be between 77 and 89 minutes is .

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