(PRINT YOUR NAME WITH UPPER CASE LETTERS. UNDERLINE YOUR LAST NAME TWICE)

(2) On lined paper rework every question where you lost points. You should either write 2-3 sentences or show computations. Indicate on this cover sheet which questions you are redoing.

ON TEST 1 my score was ______

I lost _____points:

I hope to earn ____/3_ points back and bring my Test 1 score up to______points.

I hope to earn ____/4 of these points back and bring my Test 1 score up to .points.

** Do not fill in the Points earned Box

For Part I questions : Write a "4" if you did not get the question indicated correct. For Part II questions indicate the number of points lost.

PART I MASTERY PROBLEMS. REDO THE PROBLEMS FOR WHICH YOU LOST POINTS

____1. If there are 90 items in a box, how many samples of 3 can we choose without replacement?

______2. P(A) = 0.7 , P(B) = 0.8 , P(AÇB)= 0.55. P(AÈB) =____.

____ 3. Suppose we toss a single die and the result is the number of dots observed. Then

S={1,2,3,4,5,6}. Let A= {an even number of dots}, and let

B={the number of dots is less than 5} .

Then __________.

___ 4. P(AÇ B)= 0.5 P(A)=0.6 P(B)= 0.8, P(B|A)=

(a) 0.6

(b) 6/8=0.75

(c) 5/6=0.833

(d) 5/8=0.625

　

___ 5. Given S= {1,2,3,4,5,6} the outcomes of the toss of 1 die.

Let A={we get 1 dot} and let B={we get less than 2 dots}. Which statement below is correct?

(a) A and B independent events. A and B are mutually exclusive events.

(b) A and B are dependent events. A and B are mutually exclusive event.

(c) A and B are independent. A and B are not mutually exclusive.

(d) A and B are dependent events. A and B are not mutually exclusive.

___6. P(B|A) =0.8 P(A)=0.25 P(B)=0.4 P(AÇ B)= ______

　

____7. Given the values for F(x), the distribution of X. Find P(X=3.0).

x 0 0.5 1.0 1.5 2.0 3.0

F(x) 0.2 0.4 0.45 0.6 0.9 1.0

______ 8. Given that X has binomial probability distribution with p=0.1 and n=25, what is the value of s , the standard deviation of X?

_____9. Evaluate

_____ 10. X has Poisson distribution with l =2. Use Table 2 to find P(X>1).

_____11. If A and B are independent and P(A) >0 and P(B) >0 then which of the following is true?

P(A|B) = 1- P(A|B’)

P(A|B)=P(A|B’)

(c) P (A|B)= P(B|A)

(d) A, B are mutually exclusive

______ 12. Given the values of X and f (x) below. Find the value of s

X -3 -2 0 4

f(x) 0.1 0.2 0.3 0.4

II- 1. The probability that Laboratory A will make an error equals 0.05 and the probability that Laboratory B will make an error equals 0.05, the probability that Laboratory A and B will both make errors equals 0.002.

(a) Are the laboratories independent with respect to whether or not they make an error?

(b) What is the probability that at least one laboratory makes an error?

(c) What is the probability that Laboratory A makes an error and Laboratory B does not make an error?

(d) What is the probability that both laboratories make an error?

II-2. The distribution of waiting time at a traffic light is found to have mean equal to 5 minutes (m =5) and standard deviation equal to 0.5 minutes (s =0.5). Use Chebyshev’s Theorem to answer the following questions.

What is the upper bound to the fraction of waiting times that will deviate from 5 minutes by 1.5 minute or more?

What is the interval over which we will observe at least 90% of the waiting times?

What is the lower bound to the probability that the waiting times will be between 3 minutes and 7 minutes?

II-3. Mr. M. owns a car showroom that is visited by many people every day. The probability that a person who enters his showroom buys a car equals 0.20. Suppose we sample n=10 visitors to the showroom. We assume that the probability distribution of the visitors who purchase a car, X, is binomial.

What is the mean value of X, the number of visitors in a sample of 10 who purchase a car?

What is the standard deviation of X, the number of visitors in a sample of 10 who purchase a car?

What is the standard deviation of Y, the number of visitors in a sample of 10 who do not purchase a car?

What is the probability that EXACTLY 2 visitors in a sample of 10 purchases a car?

(e) What is the probability that more than 6 visitors in a sample of 10 purchase a car?

(f) Suppose that on a particular day we have more than 6 visitors in 10 buy a car, what should we conclude about this day? (Hint: use the result in (e))?

II-4 Prove P (AÈ BÈ C) = P (A) + P (B) – P(C) -P (A Ç B) - P (A Ç C)- P (B Ç C) + P (A Ç B Ç C).