Exam 9: Sampling Distributions

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 less than 0.58 is

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 between 0.65 and 0.73?

In an effort to identify the true proportion of college freshman who are under 18 years of age, a random sample of 500 freshmen was taken.Fifty of them were under the age of 18.The value 0.10 is a point estimate of the true proportion of freshman under age 18.

The standard error of the difference is equal to the standard error of the difference .

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:

Consider an infinite population with a mean of 160 and a standard deviation of 25.A random sample of size 64 is taken from this population.The standard deviation of the sample mean equals:

As a general rule, the normal distribution is used to approximate the sampling distribution of the sample proportion only if:

Poker Time The amount of time spent by American adults playing Poker per week is normally distributed with a mean of 4 hours and standard deviation of 1.25 hours. -{Poker Time Narrative} Find the probability that if four American adults are randomly selected, all four play Poker for more than 5 hours per week.

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

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.

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.

A sample of size 40 is taken from an infinite population whose mean and standard deviation are 68 and 12, respectively.The probability that the sample mean is larger than 70 equals

If all possible samples of size n are drawn from an infinite population with standard deviation 8, then the standard error of the sample mean equals 1.0 if the sample size is 64.

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

The variance of is ____________________.

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

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?

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:

The standard deviation of is also called the: