Exam 9: Sampling Distributions

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 a randomly selected American adult plays Poker for more than 5 hours per week.

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} Find the mean and standard error of the sampling distribution of the sample mean.

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.

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

Let X be a binomial random variable with n = 100 and p = 0.7.Approximate the following probabilities,using the normal distribution. a.P(X = 75) b.P(X ≤ 70) c.P(X > 70)

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

The standard deviation of the sampling distribution of is also called the:

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} Assume that the chairman is correct and p = 0.70.What is the sampling distribution of the sample proportion ? Explain.

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 sampling distribution of the sample mean difference ? Explain.

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 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 mean of the difference is equal to:

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} If the population standard deviation is $800,compute the standard error both with and without using the finite population correction factor.

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

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 two randomly selected fences are both under 54 inches.

In general,the binomial probability P(X ≤ x)is approximated by the area under the normal curve to the left of x + .5.

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.

The finite population correction factor should be used:

The variance of is ____________________.

Given an infinite population with a mean of 75 and a standard deviation of 12,the probability that the mean of a sample of 36 observations,taken at random from this population,is less than 78 is: