PROBLEM 3: Expected Value (50 POINTS)

You are seeking to start your own private security firm but you need investors. You are offering a business deal for potential security investors if they invest $100,000. You tell the potential investor that there is a 3% chance of making $200,000; 7% chance of making $140,000; an 11% chance of making $100,000; and 63% chance of making $0. How much should the potential private security firm investor be willing to pay for this deal? Do you think the potential private security firm investor would actually pay that much? Why or why not? [Show your work]

PROBLEM #4: Expected Value (50 POINTS)

You have been offered a business deal if you invest $50,000. You estimate that there is a 7% chance of making $100,000; 12% chance of making $75,000; a 23% chance of making $90,000; and 77% chance of making $0. How much should you be willing to pay for this deal? Do you think you would actually pay that much? Why or why not? [Show your work]

PROBLEM #5: BINOMIAL DISTRIBUTION (50 POINTS)

The firearms manufacturer that sells its firearms to the local sheriffs department has 2000 used firearms to sell. Each used firearm has a 13% probability of needing major mechanical repairs. You randomly select 600 firearms for potential purchase.

What is the likelihood that 39 firearms will need major mechanical repairs? [Show your work]

What is the likelihood that all the firearms will work? [Show your work]

What is the likelihood that all the firearms will need major mechanical repairs? [Show your work]

PROBLEM #6: BINOMIAL DISTRIBUTION (50 POINTS)

A bulletproof vest manufacturer has 1000 bulletproof vests for sale. Each vest has a 5% probability of experiencing a failure resulting in a serious injury or death. You randomly select 200 vests for potential purchase.

What is the likelihood that 10 vests will experience a failure resulting in a serious injury or death? [Show your work]

What is the likelihood that they will all be free from defect? [Show your work]

What is the likelihood that they will all experience a failure resulting in serious injury or death? [Show your work]

PROBLEM #7: HYPOTHESIS TESTING (50 POINTS)

The badge fabricator the sells all badges to county law enforcement agencies claims each of its badges contains exactly 60.00 milligrams of precious metal. You sample 38 badges and find that the X = 41 milligrams and s = 1.60 milligrams. Should the companys claim be rejected? Will you use a one-tail test or a two-tail test? Why? Test at = 0.05. [Show your work including graphs]

PROBLEM #8: HYPOTHESIS TESTING (50 POINTS)

The battery manufacturer that makes the batteries for the municipal police departments body cameras asserts its lithium batteries last at least 16,000 hours. You sample 200 batteries and find that the X =13,000 hours and s = 600 hours. Should the companys claim be rejected? Will you use a one-tail test or a two-tail test? Why? Test at = 0.05. [Show your work including graphs]

PROBLEM #9: TWO-SAMPLE TEST FOR THE PROPORTION (50 POINTS)

Effect of antibiotics to prevent infection caused by bacteria for gunshot wound victims.

Test at =.05

Of gunshot wound victims receiving antibiotics: 21/1000 developed an infection caused by bacteria [Show your work including graphs]

Of gunshot wound victims not receiving antibiotics: 81/1500 developed an infection caused by bacteria [Show your work including graphs]

PROBLEM #10: TWO-SAMPLE TEST FOR THE PROPORTION (50 POINTS)

Effect of NSAIDs (such as ibuprofen) on injured law enforcement personnel to decrease fever, pain, and swelling.

Test at =.05

Of injured law enforcement personnel receiving NSAIDs: 14/200 developed fever, pain, and swelling [Show your work including graphs]

Of injured law enforcement personnel not receiving NSAIDs: 54/300 developed fever, pain, and swelling. [Show your work including graphs]