Exam 8: Sampling Distributions

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

The variance of is ____________________.

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. -What is the probability that the mean age is at most 73 years?

The expected value of is ____________________.

In general, the binomial probability P(X = x) is approximated by the area under a normal curve between x- .5 and x + .5.

Mean Salary: In order to estimate the mean salary for a population of 500 employees, the president of a certain company selected at random a sample of 40 employees. -If the population standard deviation is $800, compute the standard error both with and without using the finite population correction factor.

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?

A sample of size 25 is selected from a population of size 75. The finite population correction needed to find the standard error of .

The continuity correction factor adds and subtracts the number ____________________ to/from x to find P(X = x).

The standard deviation of the sampling distribution of is also called the:

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.

If all possible samples of size n are drawn from a normal population, the probability distribution of the sample mean is an exact normal distribution.

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.

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

The finite population correction is not needed if the population size is large relative to the sample size. As a rule of thumb, we will treat any population that is at least ____________________ times larger than the sample size as large.

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?

Number of Fish Tanks: The following data give the number of fish tanks owned for a population of 4 families. -List all possible samples of 2 families that can be selected without replacement from this population, and compute the sample mean for each sample.

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.

Sampling distributions describe the distributions of: