Exam 9: Sampling Distributions

NARRBEGIN: Retirees 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.NARREND -{Retirees Narrative} What is the probability that two randomly selected retirees are over 73 years of age?

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 in computing the standard error of the sample mean, the finite population correction factor is used only if the:

The standard error of the difference $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ is equal to the standard error of the difference $\bar { X } _ { 2 } - \bar { X } _ { 1 }$ .

NARRBEGIN: PokerTime 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.NARREND -{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.

Suppose the ages of students in your program follow a positively skewed distribution with mean of 24 years and a standard deviation of 4 years. If we randomly sampled 100 students, which of the following statements about the sampling distribution of the sample mean age is NOT true?

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

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

NARRBEGIN: Average Annual Revenue 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.NARREND -{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?

The variance of $\tilde{ p }$ is ____________________.

The finite population correction factor should be used:

NARRBEGIN: CFO's Salary CFO's Salary Suppose that the starting salaries of female CFO's have a positively skewed distribution with mean of $56,000 and a standard deviation of $12,000. The starting salaries of male CFO's are positively skewed with a mean of $50,000 and a standard deviation of $10,000. A random sample of 50 female CFO's and a random sample of 40 male CFO's are selected.NARREND -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 betweenand. b.Find the probability that the mean of the first sample is smaller than the mean of the second sample.

Random samples of size 49 are taken from an infinite population whose mean is 300 and standard deviation is 21. The mean and standard error of the sample mean, respectively, are:

If a random sample of size n is drawn from a normal population, then the sampling distribution of the sample mean $\bar { X }$ will be:

NARRBEGIN: Heights of Men 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.NARREND -{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?

In a given year, the average annual salary of a NHL hockey player was $205,000 with a standard deviation of $24,500. If a simple random sample of 50 players was taken, what is the probability that the sample mean will exceed $210,000?

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:

To find the binomial probability P(X $\le$ 4) we calculate the area under the normal curve to the ____________________ (left/right) of the number ____________________.

NARRBEGIN: Barack Obama 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.NARREND -{Barack Obama Narrative} What is the probability that the number of voters in the sample who will vote for Barack Obama in the year 2012 is between 340 and 350?

NARRBEGIN: Magazines 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.NARREND -{Magazines Narrative} What is the probability that the sample mean is between 2,000 and 2,300 magazines?