Exam 9: Sampling Distributions

A sample of size 25 is selected from a population of size 500.The finite population correction is needed to find the standard error of .

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 to the right of

The Central Limit Theorem permits us to draw conclusions about a population based on a sample alone,without having any knowledge about the distribution of that population.And this works no matter what the sample size is.

Two samples are selected independently from two normal populations and the mean and standard error of the sampling distribution of are 32 and 38.72,respectively.Calculate P( > 0).

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} 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?

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?

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

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

A sampling distribution is a probability distribution for a statistic,not a parameter.

Suppose that 100 items are drawn from a population of manufactured products and the weight,X,of each item is recorded.Prior experience has shown that the weight has a non-normal probability distribution with μ = 8 ounces and σ = 3 ounces.Which of the following is true about the sampling of ?

Temporary Worker Productivity A temporary worker productivity is normally distributed.One worker produces an average of 84 units per day with a standard deviation of 24.Another worker produces at an average rate of 74 per day with a standard deviation of 25. -{Temporary Worker Productivity Narrative} What is the probability that during one week (5 working days),worker 1 will outproduce worker 2 on average?

Which of the following is true regarding the sampling distribution of the mean for a large sample size? Assume the population distribution is not normal.

The amount of bleach a machine pours into bottles has a mean of 50 ounces with a standard deviation of 0.25 ounces.We take a random sample of 36 bottles filled by this machine.The sampling distribution of the sample mean has a mean of 50 ounces.

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.

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} Describe the shape of the sampling distribution of the sample mean in this case.

Because the value of the ____________________ varies randomly from sample to sample,we can regard it as a new random variable created by sampling.

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.

If two random samples of size 36 each are selected independently from two populations with variances 25 and 16,then the standard error of the sampling distribution of the sample mean difference, ,is 5 − 4 = 1.

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 number of throws of a fair die increases,the probability that the sample mean is close to (the number)____________________ increases.