1. Central Limit Theorem for Sums Suppose random samples of n=49 are collected from an unknown distribution with the properties =43 and =3.

a. Determine the mean of X?____.

b. Determine the standard deviation of X?_____. (Include four decimal places.)

2. Application of The Central Limit Theorem for Sums 100 North Main Street is the tallest building in Winston-Salem, NC standing at 460ft tall (5520inches). Use the scenario above to determine the selected probabilities below. You may wish to use the Normal Distribution Calculator hosted by the University of Iowa's Department of Mathematical Sciences. Remember: the formatting of this calculator may vary slightly from what is used in class.

a.Given that the heights of American women follow the distribution N(65,3.5), what is the probability of that a random sample of 85 women, stacked head-to-foot, would be at least as tall as 100 North Main Street? P(X5520)=___ (Include three decimal places.)

b. Determine the z-score of X=5520 for a sample of 85. z= _____ (Include three decimal places.)

3. The average time to run the 5K fun run is 21 minutes and the standard deviation is 2.6 minutes. 46 runners are randomly selected to run the 5K fun run. Round all answers to 4 decimal places where possible and assume a normal distribution.

a.What is the distribution of XX? ~ N(___,___)

b.What is the distribution of xx? ~ N(___,___)

c.What is the distribution of x? x ~ N(__,____)

d.If one randomly selected runner is timed, find the probability that this runner's time will be between 20.925 and 21.425 minutes. ___?

e.For the 46 runners, find the probability that their average time is between 20.925 and 21.425 minutes.___?

f.Find the probability that the randomly selected 46 person team will have a total time less than 975.2.____?

g.For parts e) and f), is the assumption of normal necessary? Yes?No?

h.The top 10% of all 46 person team relay races will compete in the championship round. These are the 10% lowest times. What is the longest total time that a relay team can have and still make it to the championship round?_____ minutes?