Exam 9: Sampling Distributions

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 mean of the sampling distribution of the sample proportion , when the sample size n = 100 and the population proportion p = 0.92, is 92.0.

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 shape of the sampling distribution of the sample mean number of magazines sold per day? Why?

If all possible samples of size n are drawn from an infinite population with a mean of 15 and a standard deviation of 5, then the standard error of the sample mean equals 1.0 for samples of size:

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?

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?

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:

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. -{Mean Salary Narrative} Would you use the finite population correction factor in calculating the standard error of the sample mean in this case? Explain.

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 between

For sample sizes greater than 30, the sampling distribution of the mean is approximately normally distributed:

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?

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, their average number of hours spent playing Poker is more than 5 hours per week.

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

Suppose X has a distribution that is not normal.The Central Limit Theorem is important in this case because:

The estimator of the probability of success in a binomial distribution is: ____________________.

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?

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. -{CFO's Salary Narrative} What is the probability that the sample mean salary of male CFO's will not exceed that of the female CFO's?

A sample of 250 observations is selected at random from an infinite population.Given that the population proportion is .25, the standard error of the sampling distribution of the sample proportion is:

DVD Rental Store A DVD rental store wants to know what proportion of its customers are under age 21.A simple random sample of 500 customers was taken, and 375 of them were under age 21.Presume that the true population proportion of customers under age 21 is 0.68. -{DVD Rental Store Narrative} Describe the shape of the sampling distribution of proportion of customers who are under age 21.

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} Assume that Gore is correct and p = 0.65.What is the sampling distribution of the sample proportion ? Explain.