Let X1,..., X16 be an independent trials process of continuous random variables with common mean 9 and common variance 400. Let S16 be their sum and A16 be their average. Use the Central Limit Theorem to estimate the following: P(-6.39999999999998 < S16 < 175.2). P(-0.300000000000001 < A16 < 13.25). (give your answer to four decimal places) # (give your answer to four decimal places)

Assume that the height of male students in a large university is normally distributed with mean 172.7 cm and variance 57.76 cm². (a) Suppose 80 random samples, each with 25 male students are obtained. In how many samples would you expect the sample mean to be between 169.66 cm and 173.46 cm? Give you answer to one decimal place. Answer: number of samples = (b) Suppose 6 random samples, each with 25 male students are obtained. Compute the probability that exactly 4 of the 6 samples will have its sample mean between 169.66 cm and 173.46 cm. Give your answer to two decimal places. Answer: probability=

The U.S. Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National Park) from 1870 to 1987. Let x1 be a random variable that represents the time interval (in minutes) between Old Faithful eruptions for the years 1948 to 1952. Based on 9180 observations, the sample mean interval was x1 = 62.6 minutes. Let x2 be a random variable that represents the time interval in minutes between Old Faithful eruptions for the years 1983 to 1987. Based on 24,872 observations, the sample mean time interval was x2 = 70.0 minutes. Historical data suggest that σ1 = 8.91 minutes and σ2 = 11.78 minutes. Let μ1 be the population mean of x1 and let μ2 be the population mean of x2. (a) Compute a 95% confidence interval for μ1 – μ2. (Use 2 decimal places.) lower limit       upper limit       (b) Comment on the meaning of the confidence interval in the context of this problem. Does the interval consist of positive numbers only? negative numbers only? a mix of positive and…

The test scores on a placement exam are normally distributed random variables with a mean of 104 and standard deviation of 12. 12) Find the probability that a selected test score is less than 117 [[0.8599]] 13) Find the probability that a selected test score is between 92 and 122 [[0.7745]] 14) Find the placement test score that has 75% of the other scores below it. [[104 + 0.67(12) = 112.04]]