Exam 7: Sampling Distributions

The Central Limit Theorem is considered powerful in statistics because it works for any population distribution provided the sample size is sufficiently large and the population mean and standard deviation are known.

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

Instruction 7-1 Times spent studying by students in the week before final exams follow a normal distribution with a standard deviation of 8 hours.A random sample of 4 students was taken in order to estimate the mean study time for the population of all students. -Referring to Instruction 7-1,what is the probability that the sample mean differs from the population mean by less than 2 hours?

Since a ________ is not a randomly selected probability sample,there is no way to know how well it represents the overall population.

Instruction 7-1 Times spent studying by students in the week before final exams follow a normal distribution with a standard deviation of 8 hours.A random sample of 4 students was taken in order to estimate the mean study time for the population of all students. -Referring to Instruction 7-1,what is the probability that the sample mean is more than 3 hours below the population mean?

Why is the Central Limit Theorem so important to the study of sampling distributions?

Instruction 7-1 Times spent studying by students in the week before final exams follow a normal distribution with a standard deviation of 8 hours.A random sample of 4 students was taken in order to estimate the mean study time for the population of all students. -Referring to Instruction 7-1,what is the probability that the sample mean differs from the population mean by more than 3 hours?

Sales prices of matchbox cars from the 1960s are known to possess a skewed-right distribution with a mean sale price of $5.25 and a standard deviation of $2.80.Suppose a random sample of 100 cars from the 1960s is selected.Describe the sampling distribution for the sample mean sale price of the selected cars.

Instruction 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 Instruction 7-4,90% of the samples will have more than what percentage of customers who will make a purchase after visiting the web site?

A manufacturer of power tools claims that the average 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.So,95% of the sample means based on samples of size 64 will be between ________ and ________.

The standard error of the mean for a sample of 100 is 30.What is the standard deviation?

A manufacturer of power tools claims that the average 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 standard deviation of the sampling distribution of the sample mean is ________ minutes.

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

The amount of pyridoxine (in grams)per multiple vitamin is normally distributed with μ = 110 grams and σ = 25 grams.A sample of 25 vitamins is to be selected.What is the probability that the sample mean will be between 100 and 120 grams?

Instruction 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 Instruction 7-4,90% of the samples will have less than what percentage of customers who will make a purchase after visiting the web site?

The amount of bleach a machine pours into bottles has a mean of 1080 grams with a standard deviation of 4.5 grams.Suppose we take a random sample of 36 bottles filled by this machine.The probability that the mean of the sample is between 1078.2 and 1079.4 grams is ________.

A manufacturer of power tools claims that the average 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 greater than 88 minutes is ________.

Items or individuals in a judgement sample are chosen with regard to their probability of occurrence.

The owner of a fish market has an assistant who has determined that the weights of rainbow trout are normally distributed,with mean of 3.2 kilograms and standard deviation of 0.8 kilogram.If a sample of 25 fish yields a mean of 3.6 kilograms,what is the Z-score for this observation?

A study at a university in New South Wales reveals that,historically,45% of their students are minority students.If random samples of size 75 are selected,95% of the samples will have more than ________% of minority students.