al Probability Distributions 10. The annual snowfall (in feet) for a central New York state county P(x) 1-5.8 =2.3 0.12 0.04+ (a) 2 f M 10 Snowfall (in feet) =0.58 (b) -0.23 H=5.8 = 0.23 -0.5 0 0.5 1.0 1.5 Snowfall (in feet) 246 7 8 10 Snowfall (in feet) (c) M-5.8 =2.3 A -2 0 2 4 6 8 10 12 Snowfall (in feet) A Sampling Distribution of Sample Means In Exercises 11-14, a population and sample size are given. (a) Find the mean and standard deviation of the population. (b) List all samples (with replacement) of the given size from the population and find the mean of each. (c) Find the mean and standard deviation of the sampling distribution of sample means and compare them with the mean and standard deviation of the population. 11. The load-bearing capacities (in thousands of pounds) of five transmission line insulators are 64, 48, 19, 79, and 56. Use a sample size of 2. 12. The diameters (in inches) of four machine parts are 1.000, 1.004, 1.001, and 1.003. Use a sample size of 2. 13. The melting points (in degrees Celsius) of three industrial lubricants are 350, 399, and 418. Use a sample size of 3. 14. The lifetimes (in hours) of four diamond-tipped cutting tools are 70, 85, 81, and 67. Use a sample size of 3. Finding Probabilities In Exercises 15-18, the population mean and standard deviation are given. Find the indicated probability and determine whether the given sample mean would be considered unusual. 15. For a random sample of n = 64, find the probability of a sample mean being less than 24.3 when = 24 and = 1.25. 16. For a random sample of n = 100, find the probability of a sample mean being greater than 24.3 when = 24 and = 1.25. 17. For a random sample of n = 45, find the probability of a sample mean being greater than 551 when u = 550 and = 3.7. 18. For a random sample of n = 36, find the probability of a sample mean being less than 12,750 or greater than 12,753 when = 12,750 and = 1.7.