Exam 9: Sampling Distributions

A CPA knows from past history that the average accounts receivable for a company is $521.72 with a standard deviation of $584.64.If the auditor takes a simple random sample of 100 accounts,what is the probability that the mean of the sample is within $120 of the population mean?

Random samples of size 81 are taken from an infinite population whose mean and standard deviation are 45 and 9,respectively.The mean and standard error of the sampling distribution of the sample mean are:

Given a binomial distribution with n trials and probability p of a success on any trial,a conventional rule of thumb is that the normal distribution will provide an adequate approximation of the binomial distribution if

The standard error of the difference between sample means, ,is calculated by the formula where is the variance of population i (i = 1,2).

Sampling distributions describe the distributions of:

Number of Fish Tanks The following data give the number of fish tanks owned for a population of 4 families. ​ ​ -{Number of Fish Tanks Narrative} Find the sampling distribution of ,and use it to calculate the mean and the standard deviation of .

Average Annual Revenue Suppose that the average annual revenue of a small business is $150,000 with a standard deviation of $40,000.Assume that the revenue distribution is normal. ​ ​ -{Average Annual Revenue Narrative} What is the probability that the average annual revenue of a random sample of 4 businesses is less than $120,000?

As the size of the sample is increased,the mean of increases.

Given that X is a binomial random variable with very large n,the binomial probability P(X ≤ 5)is approximated by the area under a normal curve to the left of

Two random samples of sizes 30 and 36 are selected independently from two populations with means 80 and 88,and standard deviations 15 and 20,respectively. a.Find the standard error of the difference between and . b.Find the probability that the mean of the first sample is smaller than the mean of the second sample.

Heights of Men The heights of men in the USA are normally distributed with a mean of 68 inches and a standard deviation of 4 inches. ​ ​ -{Heights of Men Narrative} A random sample of five men is selected.What is the probability that the sample mean is greater than 70 inches?

The normal approximation to the binomial distribution gets better and better as ____________________ increases.

If a simple random sample of 300 observations is taken from a population whose proportion p = 0.6,then the expected value of the sample proportion is 0.60.

Graduate Internships The chairman of the Biology department in a certain college believes that 70% of the department's graduate internships are given to international students.A random sample of 50 graduate interns is taken. ​ ​ -{Graduate Internships Narrative} What is the probability that the sample proportion is within ±.05 of the population proportion p?

Barack Obama Bill Clinton,the former President of the United States,believes that the proportion of voters who will vote for Barack Obama in the year 2012 presidential elections is 0.65.A sample of 500 voters is selected at random. ​ ​ -{Barack Obama Narrative} Find the expected value and the standard deviation of the sample proportion .

Suppose that the probability p of success on any trail of a binomial distribution equals 0.90.Then for which of the following number of trials,n,would the normal distribution provide a good approximation to the binomial distribution?

Magazines A local magazine store sells an average of 2,100 magazines per day,with a standard deviation of 500 magazines.Consider a sample of 60 days of operation. -{Magazines Narrative} What is the probability that the sample mean is between 2,000 and 2,300 magazines?

Retirees A sample of 50 retirees is drawn at random from a normal population whose mean age and standard deviation are 75 and 6 years,respectively. ​ ​ -{Retirees Narrative} What is the probability that the mean age exceeds 73 years?

The width of the sampling distribution of gets ____________________ as the sample size increases.

The probability of success on any trial of a binomial experiment is 20%.Find the probability that the proportion of success in a sample of 400 is: a.less than 18%. b.more than 18%. c.between 18% and 22%.