sample of 31 years of rainfall for California and a sample of 49 years of rainfall for New York has been taken. (a) Show the probability distribution of the sample mean annual rainfall for California. -21-14-07 0 0.7 14 21 199 200 21.3 22 22.7 234 24.1 inches inches Assume that the standard deviation for both states is 4 inches. A ^^ inches 39.9 40.6 413 42 42.7 434 44.1 @O 10 14 18 22 (b) What is the probability that the sample mean is within 1 inch of the population mean for California? (Round your answer to four decimal places) (c) What is the probability that the sample mean is within 1 inch of the population mean for New York? (Round your answer to four decimal places) 26 30 34 inches

The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60000 miles and a standard deviation of 1400 miles. What is the probability that the average life of 4 tires is greater than 58,600 miles?

# of Hurricanes from 1850-1920 year,#hurricanes.   1850,2 1860,1 1870,1 1880,4 1890,4 1900,2 1910,6 1920,8   Mean: 3.500 Standard Deviation: 2.507   # of Hurricanes from 1930-2000 year,hurricanes.       1930,16 1940,9 1950,15 1960,14 1970,8 1980,10 1990,14 2000,23   Mean: 13.625 Standard Deviation: 4.809   1. Calculate the Z score for the difference of the means.

The life expectancy of a fluorescent tube is normally distributed with a mean of 6,050 hours and a standard deviation of 800 hours. Find the probability that a tube lasts for more than 6,850 hours. Use the Empirical Rule. Empirical Rule for a Normal Distribution In a normal distribution, approximately - 68% of the data lie within 1 standard deviation of the mean. • 95% of the data lie within 2 standard deviations of the mean. - 99.7% of the data lie within 3 standard deviations of the mean. A normal distribution 0.15 2.35% 13.5% 34% 34% 13.5% 2.35% O.15 H- 30 u - 20 H +20 u +30 68% of the data 95% of the data 99.7% of the data