Sampling Distribution of a Proportion

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Questions

• What proportion of sample means would fall between a population mean of 600 and a sample mean of 800 if the standard error of the mean was 250? I need to know how to get to the solution. The final answer is: 0.2881?
• What is the mean value for this sampling distribution?
• What is the probability that a simple random sample will provide a sample of mean within 3 weeks of the population mean?
• The time #x# a student spends learning a software package is normally distributed with a mean of 8 hours and a standard deviation of 1.5 hours. What is the probability that the average learning time for 5 students exceeds 8.5 hours?
• The distribution of scores for the third exam in a Statistics course has a mean of 74 and a standard deviation of 15. A random sample of 36 exam papers is selected. What is the probability that the average score is higher than 77?
• When does the standard error of the mean decrease?
• What happens to the standard error each time you quadruple the sample size?
• What is the standard error of the mean for σ = 32, n = 16?
• A coal company wants to determine a 95% confidence interval estimate for the daily tonnage of coal that they mine. Assuming that the standard deviation of daily output is 200 tons, how many days should they sample so that the margin of error is 39.2 tons?
• What is the relationship between the standard error of the mean and the sample size?
• He time it takes for climbers to reach the highest point of a mountain is normally distributed with a standard deviation of 0.75 hours. If a sample of 35 people is drawn randomly from the population, what would be the standard error of the mean?
• Why is a sample statistic a random variable?