Exam 9: Sampling Distributions

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

The amount of time it takes to complete a final examination is negatively skewed distribution with a mean of 70 minutes and a standard deviation of 8 minutes.If 64 students were randomly sampled,the probability that the sample mean of the sampled students exceeds 73.5 minutes is approximately 0.

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?

In general,the binomial probability P(X = x)is approximated by the area under a normal curve between x − .5 and x + .5.

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

The mean of the difference is equal to the mean of the difference .

The standard error of the mean for a sample of 100 is 25.In order to cut the standard error of the mean in half (to 12.5)we must:

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 in any single day worker 1 will outproduce worker 2?

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 the mean height of a random sample of 36 men is greater than 70 inches?

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} What is the probability that the sample proportion is within 0.03 of the true proportion of customers who are under age 21?

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

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} Find the mean and standard deviation of .

If two random samples of sizes n₁ and n₂ are selected independently from two populations with means μ₁ and μ₂,then the mean of equals:

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} Find the expected value and the standard error of the sampling distribution of .

Which of the following is true about the sampling distribution of the sample mean?

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} Find the expected value of the sample mean difference.