--%>
Assignment Help - homework help

Analysing the Probabilities

1. In the waning seconds of Superbowl XLVII, the Baltimore Ravens elected to take a safety rather than punt the ball. A sports statistician wishes to analyze the effect this decision had on the probability of winning the game.

(a) Which two of the following probabilities would most help the statistician perform his analysis? P(Win¦Safety); P(Safety¦Win); P(Punt¦Win); P(Win¦Punt); P(Win); P(Win∩Safety), P(Win∩Punt)?

(b) Define (in words) what the probabilities that you selected in part (a) mean and explain (in words) why they would be useful to the analysis.

2. Let A1;A2, and A3 be events in Ω. Show that P(A1 ∩ A2 ∩ A3) = P(A1¦A2 ∩ A3)P(A2¦A3)P(A3).

3. Let A and B be events such that P(A) > 0 and P(B) > 0. Show that P(AjB) = 1 - P(A¦B)

4. A business is keeping track of how many of two parts A and B are ordered, and whether those orders are completed on time or late. The data is in the table below.

1373_mandeep.png

(a) Find c1 and c2.

(b) Do type of part ordered and delivery time appear to be independent?

(c) A customer calls and angrily complains that the part he ordered was late without giving any more details. Which type of part did the customer most likely order?

5. A medical company is developing a new test for breast cancer. Based on lab results, the test appears to have 90% specicity (the percentage of all women without the disease that the test correctly identies) and 95% sensitivity (the percentage of all women with the disease that the test correctly identies). Suppose that 12% of women who take this test have breast cancer.

(a) What is the false positive rate for this test?

(b) What is the false negative rate for this test?

(c) How will the false positive and false negative rates for this test be a ected if the percentage of women with breast cancer decreases?

6. An urn contains a red ball, a white ball, a green ball, and a plaid ball. A single ball is randomly drawn from the urn. Let A be the event that either the red ball or the plaid ball is drawn, let B be the event that either the white ball or the plaid ball is drawn, and let C be the event that the green ball or the plaid ball is drawn.

(a) What is P(A υ B υ C)?

(b) Are A, B, and C independent from each other?

(c) Are A, B, and C mutually independent?

7. You have two decks of cards in front of you. One deck is a standard 52 card deck with four aces. The other also has 52 cards, but eight aces instead of four. You randomly choose a deck and draw two cards without replacement.

(a) What is the probability of drawing at least one ace?

(b) Given that you drew at least one ace, what is the probability that you drew from the standard deck?

 

 

 

   Related Questions in Advanced Statistics

  • Q : Problem on layout A manufacturing

    A manufacturing facility consists of five departments, 1, 2, 3, 4, and 5. It produces four components having manufacturing product routings and production volumes indicated below.   1. Generate the from-to matrix and the interaction matrix. Use a

    		•
  • Q : Analytical Report Hi I WOULD LIKE TO

    Hi I WOULD LIKE TO KNOW IF YOU CAN HELP ME TO DO THE ASSIGNMENT IN HEALTH STATISTICS THANKS

    		•
  • Q : Describe how random sampling serves

    Explain sampling bias and describe how random sampling serves to avoid bias in the process of data collection.    

    		•
  • Q : Problem related to playing cards Cards

    Cards are randomly drawn one at the time and with replacement from a standard deck of 52 playing cards. (a) Find the probability of getting the fourth spades on the 10th draw. (b) Determine the

    		•
  • Q : Conclusion using p-value and critical

    A sample of 9 days over the past six months showed that a clinic treated the following numbers of patients: 24, 26, 21, 17, 16, 23, 27, 18, and 25. If the number of patients seen per day is normally distributed, would an analysis of these sample data provide evid

    		•
  • Q : Statistics Homework with SAS File is

    File is attached, need it by 8:30 AM Pacific (Seattle, WA) time. No delay acceptable. Need it March 25, 2014 on 8:30 AM Pacific time.

    		•
  • Q : Random variables Random variables with

    Random variables with zero correlation are not necessarily independent. Give a simple example.    

    		•
  • Q : Probability Distributions and Data

    1. A popular resort hotel has 300 rooms and is usually fully booked. About 4% of the time a reservation is canceled before 6:00 p.m. deadline with no penalty. What is the probability that at least 280 rooms will be occupied? Use binomial distribution to find the exact value and the normal approxi

    		•
  • Q : Statistics A nurse practitioner working

    A nurse practitioner working in a dermatology clinic is studying the efficacy of tretinoin in treating women’s post partum abdominal stretch marks. From a sample of 15 women, the mean reduction of stretch mark score is -0.33 with a sample standard deviation of 2.46. Describe what happens to the c

    		•
  • Q : Correlation Define the term Correlation

    Define the term Correlation and describe Correlation formula in brief.

    		•