Exam 9: Sampling Distributions

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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} What is the probability that a randomly selected man is taller than 70 inches?

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0.3085

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

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(0.6915)(0.6915) = 0.4782

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.

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The standard deviation of Xˉ1Xˉ2\bar { X } _ { 1 } - \bar { X } _ { 2 } is also called the:

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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, Xˉ1Xˉ2\bar { X } _ { 1 } - \bar { X } _ { 2 } , is 5-4 = 1.

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The standard deviation of the sampling distribution of Xˉ\bar { X } is also called the:

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

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NARRBEGIN: DVD Rental Store 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.NARREND -{DVD Rental Store Narrative} Find the mean and standard deviation of p~\tilde{ p } .

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

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NARRBEGIN: Temporary Worker Producti 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.NARREND -{Temporary Worker Productivity Narrative} What is the probability that in any single day worker 1 will outproduce worker 2?

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Given that X is a binomial random variable with very large n, the binomial probability P(X \ge 5) is approximated by the area under a normal curve to the right of

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NARRBEGIN: Number of Fish Tanks Number of Fish Tanks The following data give the number of fish tanks owned for a population of 4 families. Family A B C D Number af Fish Tanks Owned 2 1 4 3 NARREND -{Number of Fish Tanks Narrative} List all possible samples of 2 families that can be selected without replacement from this population, and compute the sample mean Xˉ\bar { X } for each sample.

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A sampling distribution is defined as the probability distribution of means from all possible sample sizes that are taken from a given population.

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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?

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In inferential statistics, the standard error of the sample mean assesses the uncertainty or error of estimation.

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The standard error of the mean:

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The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with a mean of 3.2 pounds and standard deviation of 0.84 pounds. If a sample of 16 fish is taken, what is the standard error of the mean weight?

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The standard deviation of p~\tilde{ p } is also called the ____________________ of the sample proportion.

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If all possible samples of size n are drawn from an infinite population with a mean of μ\mu and a standard deviation of σ\sigma , then the standard error of the sample mean is inversely proportional to:

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If all possible samples of size n are drawn from a normal population, the probability distribution of the sample mean Xˉ\bar { X } is an exact normal distribution.

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