[size=150]Let ξ = {x : 1 ≤ x < 17, xÎ N}.[br] P , Q and R are the subsets of ξ such that[br] P = {multiples of four}, Q = (factors of 36}, R = {square numbers}.[br](a) List the elements of[br] (i) ξ[br] (ii) P ^ Q ^R.                          (2) pts[br](b) Describe in words the set P v Q.                  (1) pt[br][br](c) (i) Draw a Venn diagram to show the relationship between sets P, Q and R. (2) pts[br](ii) Write the elements of ξ in the appropriate places on the Venn diagram.   (3) pts[br][br](d) Let p, q and r be the statements[br] p : x is a multiple of four;[br] q : x is a factor of 36;[br] r : x is a square number.[br](i) Write a sentence, in words, for the statement:[br] (p v r) ^ ~ q                         (2) pts[br](ii) Shade the region on your Venn diagram in part (c)(i) that represents (p v r) ^~ q (1) pt[br][br](iii) (a) Use a truth table to determine the values of (p v r) ^ ~q. Write the first three columns of your truth table in the following format.[br]p q r[br]T T T[br]T T F[br]T F T[br]T F F[br]F T T[br]F T F[br]F F T[br]F F F                            (3) pts[br](b) Write down one possible value of x for which (p v r) ^ ~q is true.      (1) pt[/size]

[size=150]A personality inventory test for passive-aggressive characteristics for 300 students. Individuals were provided with a score from 1 to 5, where 1 was very passive and 5 was very aggressive. A score of 3 indicated neutral characteristic. Based on the results of the frequency table below, construct a probability distribution for the random variable x. [br][br]Score, x:  1  2  3  4  5[br]Frequency, P(x): 48 66 84 42 60[br][br]Construct Probability Distribution Table (here)[br]x: 1 2 3 4 5[br]P(x): [/size]

[size=150]Decide whether the random variable x is discrete or continuous:[br][br]X represents the number of pumps at a gas station[/size]

[size=150]Decide whether the random variable x is discrete or continuous:[br][br]X represents the amount of time to complete a 5k race at the park.[/size]

[size=150]Decide whether the random variable x is a probability distribution. If it is not, identify the property that is not satisfied.[br][br]The random variable x represents the number of classes in which a student is enrolled in a semester at a college.[br][br]Table: -->[br] x  1  2 3  4 5 6 7 8[br]P(x) 1/80 3/75 2/10 8/25 24/20 1/6 2/24 1/60 [/size]

[size=150]Decide whether the experiment is a binomial experiment. If it is not, identify the property that is not satisfied. If it is, list the values of n, p, q, and the values that x can assume. A fair coin is tossed repeatedly until 12 heads are obtained. The random variable x counts the number of tosses. [/size]

[size=150]Find the mean, variance, and standard deviation of the Binomial Distribution with the given values of n and p. (Identify q first)[br][br]n = 80, p = 0.35[/size]

[size=150]A survey indicates that 72 percent of men in the U.S. consider watching or playing American Football their favorite leisure-time activity. You randomly select 4 U.S. men and ask them if American Football is their favorite leisure-time activity. Find the probability that exactly two of them respond yes.[/size]

[size=150]If you flip a coin 3 times, use a tree diagram to determine probability of getting two tails and one heads. [/size]

[size=150]Two cards are selected in sequence from a standard deck of 52 cards. Find the probability that the second card is a Jack, given that the first card is an Ace. (Assume the Ace is not replaced)[/size]