Assume that the population of heights of male college students is approximately normally distributed ...

1. Given the following frequency distribution, find the mean, variance, and standard deviation. Please show all of your work. Class Frequency 56-58 22 59-61 14 62-64 24 65-67 19 68-70 19 

2. The following data lists the average monthly snowfall for January in 15 cities around the US: 8 35 31 26 36 41 29 40 17 16 33 38 30 34 13 Find the mean, variance, and standard deviation. Please show all of your work. 

3. Rank the following data in increasing order and find the positions and values of both the 28th percentile and 56th percentile. Please show all of your work. 0 1 6 8 9 9 8 6 3 1 0 9 4. 

4 - For the table that follows, answer the following questions: x y 1 -1/4 2 -1/2 3 -3/4 Would the correlation between x and y in the table above be positive or negative? - Find the missing value of y in the table. - How would the values of this table be interpreted in terms of linear regression? - If a “line of best fit” is placed among these points plotted on a coordinate system, would the slope of this line be positive or negative? 

5. A set of 50 data values has a mean of 18 and a variance of 4. I. Find the standard score (z) for a data value = 20. II. Find the probability of a data value 20. Show all work. 

6. Answer the following: (A) Find the binomial probability P(x = 5), where n = 12 and p = 0.60. (B) Set up, without solving, the binomial probability P(x is at most 5) using probability notation. (C) How would you find the normal approximation to the binomial probability P(x = 5) in part A? Please show how you would calculate µ and σ in the formula for the normal approximation to the binomial, and show the final formula you would use without going through all the calculations. 

7. Assume that the population of heights of male college students is approximately normally distributed with mean of 70.07 inches and standard deviation of 6.48 inches. A random sample of 93 heights is obtained. Show all work. (A) Find P(x>70.750) (B) Find the mean and standard error of the xbar distribution (C) Find P(xbar>70.75 (D) Why is the formula required to solve (A) different than (C)?