Finding mean and standard devi

1. The following data are your company’s annual health care premium increases over the last 10 years:
5
7
12
9
15
10
10
10
9
18

a. Find the Mean

b. Find the Location of the Median

c. Find the Median

d. Find the Range

e. Find the Midrange

f. Find the Mode

g. Find the Standard Variance

h. Find the Standard Deviation.

Finding Mean and Standard Devi

You are in charge of storage at a winery. A 60 gallon barrel of wine weighs on average 120 lbs with a standard deviation of 6 lbs. One gallon of wine weighs about 8 lbs with a standard deviation of .40 lbs. You store barrels on shelves on your property.

a. What is the expected mean and standard deviation of the weight of 10 full barrels of wine?
b. You want to store 10 barrels on a shelf. Shelves have weight limits, which represent the maximum weight limit they can safely hold. What is the smallest maximum weight limit that the shelf must be able to carry such that the probability that the 10 barrels will exceed the weight limit is no more than 0.00135? Round up to the nearest pound.

Finding Mean and Standard Devi

Refere to attachment for better formula representation. Let (Y1, Y2,…Yn) be a random sample from a uniform probability density functions (p.d.f) given by:
f (y;theta) = (1-theta)^-1, theta<y<1

a. Find the mean of Y and shown that the variance of Y is (1-theta)^2/12
b. Show that theta = 2(sum Y/n) -1 is an unbiased estimator of theta.
c. Show that Var (theta0 = (1- theta)^2/3n

Finding mean and standard devi

The Globe Fishery packs shrimp that weigh more than 1.91 ounces each in packages marked” large” and shrimp that weigh less than 0.47 ounces each into packages marked “small”; the remainder are packed in “medium” size packages. If a day’s catch showed that 19.77 percent of the shrimp were large and 6.06 percent were small, determine the mean and the standard deviation for the shrimp weights. Assume that the shrimps’ weights are normally distributed.

Finding mean and standard devi

Question #1

Calculate arithmetic average returns, the variances, and the standard deviations for X and Y.
Returns
Year X Y
1 17 23
2 22 34
3 8 11
4 -15 -32
5 10 21

Question #2

What are the arithmetic and geometric returns for the stock?

Year Price Dividend Arithmetic Return Geometric Return
1 $43.15 –
2 $48.13 $0.45
3 $57.05 $0.49
4 $45.13 $0.55
5 $52.05 $0.62
6 $61.13 $0.68.