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Name:_________________________ AP Stats/ __________ Date: ___________ Date Due:_____________ AP Statistics 6.1 Homework Worksheet Discrete and Continuous Random Variables Please show all work on a separate piece of paper 1) Toss a coin 4 times. Let π = π‘βπ ππ’ππππ ππ βππππ you get a. Find the probability distribution of X b. Find π(π β€ 3) and interpret the result 2) Suppose you roll a pair of fair, six-sided dice. Let T = the sum of the spots showing on the up-faces (in other words, the sum of the two die). a. Find the probability distribution of T b. Find π(π β₯ 5 ) and interpret the result. 3) In an experiment on the behavior of young children, each subject is placed in an area of five toys. Past experiments have shown that the probability distribution of the number X of toys played with by a randomly selected subject is as follows: Number of Toys 0 1 2 3 4 5 Probability a. b. c. d. .03 .16 .30 .23 .17 .11 Find π( ππππ¦π π€ππ‘β ππ‘ πππ π‘ π‘π€π π‘ππ¦π ) Describe the event π > 3 in words. What is its probability? What is the probability that π β₯ 3? Calculate the mean of the random variable X and interpret this result in context. Calculate the standard deviation of the random variable X and interpret this result in context. 4) The normal distribution with mean π = 6.8 and π = 1.6 is a good description of the Iowa Test of Basic Skills (ITBS) vocabulary scores of seventh-grade students in Gary, Indiana. Call the score of randomly chosen student X for short. Find π(π β₯ 9) and interpret the result. 5) The weights of three year old females closely follow a Normal distribution with a mean of 30.7 pounds and a standard deviation of 3.6 pounds. Randomly choose one three year old female and call her weight X. a. Find the probability that the randomly selected three year old female weighs at least 30 pounds. b. Find the probability that the randomly selected three year old female weighs at between 27.1 and 34.3 pounds. Name:_________________________ AP Stats/ __________ Date: ___________ Date Due:_____________ 6) Choose a person aged 19 to 25 years at random and ask, βIn the past seven days, how many times did you go to an exercise or fitness center or work out?β Call the response Y for short. Based on a large sample survey, here is the probability model for the answers you get Days 0 1 2 3 4 5 6 7 Probability .68 .05 .07 .08 .05 .04 .01 .02 a. Show that this is legitimate probability distribution. b. Describe the event π < 7 in words. What is π(π < 7)? c. Make a histogram of the probability distribution, describe what you see. Consider the events π΄ = π€ππππ ππ’π‘ ππ‘ ππππ π‘ ππππ and π΅ = π€ππππ ππ’π‘ πππ π π‘βππ 5 π‘ππππ πππ π€πππ d. What outcomes make up the event A, what is P(A)? e. What outcomes make up event B, what is P(B)?