Exam 9: Sampling Distributions

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} If the population of men's heights is not normally distributed,which,if any,of the previous questions can you answer?

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} What is the probability that a randomly selected man is taller than 70 inches?

Recall the rule of thumb used to indicate when the normal distribution is a good approximation of the sampling distribution for the sample proportion .For the combination n = 50,p = 0.05,the rule is satisfied.

For a sample size of 1,the sampling distribution of the mean is normally distributed:

A sample of size 25 is selected at random from a finite population.If the finite population correction factor is 0.63,then the population size is:

The standard deviation of is also called the:

Consider an infinite population with a mean of 100 and a standard deviation of 20.A random sample of size 64 is taken from this population.The standard deviation of the sample mean equals 2.50.

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 two randomly selected retirees are over 73 years of age?

The standard error of the mean:

The standard deviation of is also called the:

If two random samples of sizes 30 and 32 are selected independently from two populations with means 121 and 109,then the mean of the sampling distribution of the sample mean difference, ,equals 12.

If two random samples of sizes 30 and 36 are selected independently from two populations with means 78 and 85,and standard deviations 12 and 15,respectively,then the standard error of the difference and is equal to:

Heights of Fences Heights of fences are normally distributed with a mean of 52 inches and a standard deviation of 4 inches. ​ ​ -{Heights of Fences Narrative} Find the probability that one randomly selected fence is under 54 inches.

In general,the binomial probability P(X ≥ x)is approximated by the area under the normal curve to the left of x − .5.

The standard error of the sampling distribution of the sample proportion ,when the sample size n = 100 and the population proportion p = 0.30,is 0.0021.

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 is at most 73 years?

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} Could you have used a normal distribution to find an (approximate)probability for the average of 4 revenues if the population of revenues did not have a normal distribution?

A sample of size 200 is taken at random from an infinite population.Given that the population proportion is 0.60,the probability that the sample proportion is between 0.58 and 0.62 is:

A sampling distribution is defined as the probability distribution of means from all possible sample sizes that are taken from a given population.

As the size of the sample is increased,the standard error of decreases.