Horne Insert Draw Design Layout References Mailings Review View Help ProWritingAid lv'l i3 v .A E 6%}? Q 9 Font Paragraph SWIES Editing Dictate Start V V v c Realtime Undo Clipboard ii Styles Iii Voice Sensitivtty Editor ProWritingAid Part A: Let's say you open a package of Reese's pieces and find the pieces below: 1. Complete the table below. Does it seem like each color is equally represented? Hint: There should be 61 pieces total. Color Freq uency P(color) Orange Yellow Brown Total 2. Using conditional probability, find the probability ot selecting a brown candy given that you already ate all the orange ones. - The possibility of selecting a brown candy would be 15130 or .5 3. Using conditional probability, find the probability of selecting an orange candy given that you already ate all the brown ones (this is independent from #2). - The probability of selecting an orange candy is 31161 or .6139 4. Using the multiplication rule, find the probability of selecting an orange Reese's Pieces and then selecting a brown Reese's Pieces with replacement. Are these events independent or dependent? Explain your answer. - P(orange lhen brown) = P(orange) x P(brown) = (31161) x (15161) = 46513721 or 0.1250 - The two events are independent because the tirst candy that was selected was replaced, therefore it does not affect the probability of selecting a brown candy in the second selection. 5. Using the addition rule, nd the probability of selecting an orange Reese's Pieces or a yellow Reese's Pieces. Are these events mutually exclusive? Explain your answer. - P(orange or yellow) = P(orange) + P(yellow) = (31161) + (15161) = 46161 or 0.7541 - Both events are mutually exclusive because it is not possible to select a candy that is both orange and yellow at the same time. Part B: You randomly select Reese's Pieces, note if the color is orange, then replace it. You repeat this 5 times. Let X be the random variable that represents the number of orange Reese's Pieces selected. 6. Is this experiment binomial? Explain your answer. - Yes it is binomial because... '1. Using the picture of Reese's pieces above, tind p (the probability of selecting an orange candy). 8. Construct a probability distribution for the random variable X, the number of orange Reese's Pieces. (Hint: See the 5.2 Binomial Distribution notes for an example) 9. What is the probability ofselecting exactly 2 orange Reese's Pieces? 10. What is the probability of selecting at least 3 orange Reese's Pieces? 11. If we open a new package of Reese's pieces that has 53 pieces of candy in it, how many would we expect to be orange? Hint: Mean for the Binomial Distribution Part (2: Let's assume that each package has a mean of 50 pieces of candy and the standard deviation is 4 pieces of candy. Use Ch 6.1-6.2 as a reference for these questions. 12. Using the Empirical Rule, nd the number of pieces in a package that are two standard deviations away from the mean. Would we consider 43 pieces in a package unusual? Why or Why not? 13. You open a randomly selected package of candy from the store and find that it has 55 pieces of candy in it (yayl). How many standard deviations is 55 from the mean? Hint: Find the z-score 14. What is the probability that you would receive 51 pieces of candy or more in a package? Sketch the curve. Is this event likely or unlikely? 15. What is the probability that you would receive less than 45 pieces of candy in a package? Sketch the curve. 16. What is the probability that you would receive between 48 and 52 pieces of candy in a package? Sketch the curve. 326 words D2 Text Predictions: 0n ID: Focus as: s o - a n l swamps File Home Insert Draw Design Layout References Mailings Review View Help ProWritingAid lv'l l3 v Age/pi? a Font Paragraph SWIES Editing Dictate Start V V v V Realtime Undo Clipboard ii Styles El Voice Sensitlwty Editor ProertlngAid ._. Eu...\" nonhuman... pnntummy, .l.l.. u... funguwluy u. tunnel...\" t. mum. own.) 3...\". \"mt you. must...) .4\". w. mu mung\" ones. - The possibility of selecting a brown candy would be 15:60 or .5 3. Using conditional probability, find the probability of selecting an orange candy given that you already ate all the brown ones (this is independent from #2). - The probability of selecting an orange candy is 31l81 or .6739 4. Using the multiplication rule, find the probability of selecting an orange Reese's Pieces and then selecting a brown Reese's Pieces with replacement. Are these events independent or dependent? Explain your answer. - P(orange then brown) = P(orange) x P(brown) = (31l61) x (15161) = 465137'21 or 0.1250 - The two events are independent because the first candy that was selected was replaced, therefore it does not affect the probability of selecting a brown candy in the second selection. 5. Using the addition rule, find the probability of selecting an orange Reese's Pieces or a yellow Reese's Pieces. Are these events mutually exclusive? Explain your answer. - P(orange or yellow) = P(orange) + P(yellow) = (31(61) + (151'61) = 46.61 or 0.7541 - Both events are mutually exclusive because it is not possible to select a candy that is both orange and yellow at the same time. Part B: You randomly select Reese's Pieces, note if the color is orange, then replace it. You repeat this 5 times. Let X be the random variable that represents the number of orange Reese's Pieces selected. 6. Is this experiment binomial? Explain your answer. - Yes it is binomial because... 7. Using the picture of Reese's pieces above, tlnd p (the probability of selecting an orange candy). 8. Construct a probability distribution for the random variable X, the number of orange Reese's Pieces. (Hint: See the 5.2 Binomial Distribution notes for an example) 9. What is the probability ofselecting exactly 2 orange Reese's Pieces? 10. What is the probability of selecting at least 3 orange Reese's Pieces? 11. If we open a new package of Reese's pieces that has 53 pieces of candy in it, how many would we expect to be orange? Hint: Mean for the Binomial Distribution Part C: Let's assume that each package has a mean of 50 pieces of candy and the standard deviation is 4 pieces of candy. Use Ch 6.1-6.2 as a reference for these questions. 12. Using the Empirical Rule, nd the number of pieces in a package that are two standard deviations away from the mean. Would we consider 43 pieces in a package unusual? Why or Why not? 13. You open a randomly selected package of candy from the store and find that it has 55 pieces of candy in it (yayl). How many standard deviations is 55 from the mean? Hint: Find the z-score 14. What is the probability that you would receive 51 pieces of candy or more in a package? Sketch the curve. Is this event likely or unlikely? 15. What is the probability that you would receive less than 45 pieces of candy in a package? Sketch the curve. 16. What is the probability that you would receive between 48 and 52 pieces of candy in a package? Sketch the curve. 17. We ideally want the most Reese's pieces we can get in a package. How many Reese's pieces need to be in a package to contain more candy than 99% of packages? Sketch the curve. Part D: Now assume that we go out and buy 30 random packs of Reese's pieces to see if the true number of pieces in a pack is more than 50. We open each package and count the number of pieces. We nd that the mean number of candies amongst the 30 packs is 51. Remember that we are assuming the mean number of candies in a pack is 50 with a standard deviation of 4. (Refer to sections 6.3-6.4 for the following questions). 18. What is the probability that the mean number of Reese's pieces is more than 51? 19. Using the results from #18, is this event likely or unlikely? What would you think about our initial assumption that each package has 50 pieces of candy? Explain your answer. 20. Conceptually speaking, what is the difference between #14 and #13? Why do you use one formula for #14 and another for #18? 326 words D2 Text Predictions: 0n ID: Focus 4 27:: c o - a n a l e rs a most\": a