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Unformatted text preview: muttrm‘o/v MA206  Probability & Statistics
Lesson 21: The Binomial Probability Distribution 1. Kobe Bryant, All—Star guard for the Los Angeles Lakers, makes 80% of his free throws. During a ﬂee throw contest, he
will attempt 20 shots. LetX = the number of free throws that Kobe Bryant makes. A binomial distribution will help model thisscenario. X” EIwNOn’W’Q/ (/75; 20/ P51 O. 520) a. Does this “experiment” satisfy the four conditions on'page 120? Explain. ' YES [exp/mam om,,‘#ao<f) b. What is the probability that Kobe makes exactly 15 of his attempts?
PCXe/a) 5’0. mm: c. What is the probability that Kobe makes more than 18 shots?
PM 71%») a 0. 04992 _, d. What is the probability that Kobe makes at least 14 of his attempts? P(r>< iii/H) vs» (OH/"agar e. How many shots do you expect Kobe to make? What is the standard deviation of X? m): w shots .
V00: 32 50 5243.2; =1.7$§O/ «swig 2. An EOD Team has a mission success rate of 0.70. The EOD Team’s success rate is independent of the others in the
unit. Given that we have an EOD Company of 10 teams, what is the probability that the overall mission is successful? The
overall mission success is deﬁned by at least 7 of the BOD Teams accomplishing their mission. X“; “umber 0'? Show? S3‘FM! V‘wsﬁfmaﬁ
X ”V Elm/”Wad (7’75 1/0; Pi: 0‘70} PM “a: ‘7?) «w Gigi/7o 3. The probability that a patient recovers ﬁom a rare blood disease is 0.40. If 15 people are known to have contracted this
disease, what is the probability that at least 10 survive? Between 3 and 8 survive? Exactly 5 survive? X : VlW’hén’ﬁV’ “at: pcwftwia‘ witty Sittrviva
X m’B/‘mormi‘a/ (”J/5w; fa); (141/0) FO< 2m): ﬂows [(3 a X a; g”; .1: graft; a fig ﬁg “7):; (i). (WW;
P<)<::5)1f3.l‘€’5‘i 4. In 1993, President Clinton ordered a bombing raid on Iraq. The plan was to send 10 F117’s on a night mission to bomb
a suspected chemical weapons production facility. The probability of an F 117 getting shot down by Iraqi air defense
systems before reaching the target is 20%. The commander of the mission has stated that he needs at least 8 aircraft over the target to be successful. Km; nuﬂvber of (Ff/75 7‘”th I‘mGe “7" 7"?) “+563 +arj€~f X’Vﬁin om/‘(a/ ”hr/0 (0 080)
a What is the probability that all 10 aircraft make it to the arget? PM: Io):o. low b. What is the probability that between 3 and 7 (inclusive) make it to the target? P(3g xe7): 0.22.2! . c. What is the probability that the mission is successful? >(x z a): o. (9778 ...
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 Spring '10
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