From a sample with n= 36, the mean duration of a geyser's eruptions is 3.48 minutes and the standard deviation is 0.89 minutes. Using Chebychev's Theorem, determine at least how many of the eruptions lasted between 0.81 and 6.15 minutes. At least of the eruptions lasted between 0.81 and 6.15 minutes. (Simplify your answer.)

You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ=72.1σ=72.1. You would like to be 99% confident that your estimate is within 2 of the true population mean. How large of a sample size is required?

A sample of 314 patients between 38 and 82 were given a drug intended to reduce their level of cholesterol. The results were the mean reduction in cholesterol of 0.94 millimole per liter. Assume the population standard deviation is σ = 0.18. Construct a 98% C.I.

You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ=37.8σ=37.8. You would like to be 90% confident that your estimate is within 1 of the true population mean. How large of a sample size is required?

You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ=56.5σ=56.5. You would like to be 95% confident that your estimate is within 1 of the true population mean. How large of a sample size is required?

Researchers at the National Weather Center in Portland, Maine recorded the number of 90° days each year since records were first kept, starting in 1875. The number of 90° days form a normal-shaped distribution, with a mean of μ = 9.6 days and a standard deviation of σ = 1.9. To see if the data showed any evidence of climate change (and specifically global warming), they also computed the mean number of 90° days for the most recent n = 4 years and obtained a mean number of days for the past four years of x̅ = 12.25 days. Using a one-tailed test with α = .05, the researchers completed the calculations, but they need your help in drawing an appropriate conclusion. (According to their calculations, the standard error is sM = 0.95, and the sample mean of x̅ = 12.25 days corresponds to a z-score of z = 2.79.) Using the same one-tailed test (α = .05), determine if the data indicate that the past four years have had significantly more 90° days than would be expected for a random sample from…

The attached plots were constructed using a sample of 272 observations. Each observation gives the elapsed time (in minutes) of an eruption of Old Faithful geyser in Yellowstone national park. d. A sample of 6 durations have values: 4.850, 2.200, 2.900, 4.367, 1.750, 3.966. What is the mean of this sample? e. What is the standard deviation of the sample in d. if ∑ni=1x2i=74.635∑i=1nxi2=74.635?( attached as pic) f. Give the shape and parameters of the sampling distribution of the sample mean when n=272n=272 if μ=3.4μ=3.4 and σ=1.16σ=1.16. Explain how you know the shape the distribution takes on.

You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ=44.7σ=44.7. You would like to be 95% confident that your estimate is within 3 of the true population mean. How large of a sample size is required?