Summative Assessment

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

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. Score, x:  1  2  3  4  5 Frequency, P(x): 48 66 84 42 60 Construct Probability Distribution Table (here) x: 1 2 3 4 5 P(x):

Decide whether the random variable x is discrete or continuous: X represents the number of pumps at a gas station

Decide whether the random variable x is discrete or continuous: X represents the amount of time to complete a 5k race at the park.

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

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.

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

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.

If you flip a coin 3 times, use a tree diagram to determine probability of getting two tails and one heads.

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)