Find the critical value of the test and apply decision rule

As a part of a class project, your statistics instructor asks you to weigh a sample of 100 items from a shipment of 500. You are testing the null hypothesis that the mean is greater or equal to 10 lbs. You are given that the standard diviation is 0.05 lb. Accepting H0 is the same as accepting the shipment. A) using a signific ...continues

Crytic math

I need them by 20th Jan Cryptic Math p Q R S T U V W X 1. Each letter stands for one of the numbers 1 - 9. 2. S + Q = V and S is smaller than Q. 3. P = R + U. 4. In one of the diagonals, all 3 numbers are perfect squares. 5. In one of the two diagonals, (P, T, X or R, T, V) the 3 ...continues

Density Function : Median and Quartiles

The density function of a continuous variable x is given by f(x) =x; 0≤x<1 and f(x) = 2-x; 1≤x<2 a) Find p(1/2≤x≤3/2) b) Find the median and quartiles of this distribution

Mutually Exclusive and Independent Events

Can E and F be both mutually-exclusive and be independent, if they are non-zero probability events. How?

Finance : Lease or Buy?

I can lease some equipment for $3,000 annually for 6 years or purchasing it for $12,000. If I can invest money at 8% annum, how do I determine which is the better choice finacially?

Compoundng Interest : Determining Amount to Deposit to get Desired Return

If I wanted to set up a trust earning 9% compounded semi-annually so that I could withdraw $10,000 every six months, begining six months from now, for 6 years. How would I determine the amount to deposit now?

Probability : False Positive

An experimental test to detect a particular type of cancer indicates the presence of cancer in 90% of individuals known to have this type of cancer, and in 15% of individuals known to be cancer-free (false positive). One hundred individuals volunteer to take the test. Of the 100, 60 are known to have the cancer, and 40 are known ...continues

Posterior Probability

An absent-minded nurse is to give Mr. Brown a pill each day. The probability that the nurse forgets to administer the pill is 2/3. If he receives the pill, the probability that Mr. Brown will die is 1/3. If he does not get his pill, the probability that he will die is 3/4. Mr. Brown dies. What is the probability that the nurse f ...continues

Using Excel Solver : Maximizing Interest and Defining Cash-Flow Constraints

At the start of the year a company wants to invest excess cash in one-month, three-month and six-month CD’s. The company is somewhat conservative and wants to make sure it has a safety margin of cash on hand each month. (left over from previous month/ available at the outset, plus principal and interest from CD’s that have becom ...continues

Combinations : Prove Recursive Relation

Consider the recursive relationship for combinations: C(n,r) = C(n-1,r) + C(n-1,r-1) Prove this relationship algebraically using the mathematical definition of a combination, as well as that of the factorial function. Provide a logical explanation for this relationship (consider n objects as consisting of n-1 existing o ...continues