代做MDM4U CHAPTER 7 TEST PROBABILITY DISTRIBUTION帮做R编程
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CHAPTER 7 TEST
PROBABILITY DISTRIBUTION
1. Determine if a uniform, binomial, geometric or hypergeometric distribution would be the best model for each of the following experiments. Explain your reasoning. [C /2 each]
a) A sample from a batch of integrated circuit chips is integrated for defects.
b) A student randomly guesses at five multiple choice questions
c) A die is tossed and the number rolled is recorded
d) Recording the number of days on a construction site without an accident
2. In a dice game, a pair of dice is rolled, with the two numbers rolled being added together. If the two numbers rolled add to a prime number, double this number of points is received.
Otherwise the sum of the roll is subtracted from the point total.
a) Create the rolled dice table (all the options), along with a table of probabilities: [KU /4]
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ROLL SUM |
(X) POINTS |
P(X) |
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b) Determine the expected value. [KU /3]
c) Is this a fair game? Explain why or why not. [C /2]
3. A dartboard contains 16 equally-sized sectors numbered 1 to 16. A dart is randomly tossed at the board 10 times.
a) What is the probability that the dart lands in sector 12 exactly 3 times. [A /3]
b) What is the probability that the dart lands in sector 12 at least 2 times? [A /4]
c) What is the expected number of times the dart would land in sector 12? [A /2]
4. After a poll, you found that 78% of students were excited about prom.
a) What is the probability you would have to interview exactly 3 people before finding one excited about the prom? [A /2]
b) What is the probability you would have to interview at most 3 people before finding one excited about the prom. [A /3]
c) What is the expected waiting time before you find a student excited about the prom? [A /2]
5. In the Arts Club there are 14 students, 9 of whom are female. However, usually 6 students show up at each meeting.
a) What is the probability that exactly 4 of the 6 students are female? [A /3]
b) What is the expected number of females at each meeting? [A /2]
c) Explain mathematically why the probability distribution you choose to solve this problem was the most appropriate. [C /2]
6. The odds in favour of an Air Gibson flight being on time is 3:1.
a) What is the probability that this airline’s next eight flights will be on time? [T /2]
b) What is the expected waiting time before a flight delay? [T /1]
7. A teacher provides pizza for his class if they earn an A-average on any test. The probability of the class getting an A-average on one test is 8%. What is the expected waiting time before the class gets a pizza? [T /2]
8. In a mathematics class of 20 students, 5 are bilingual. If the class is randomly divided into 4 project teams. What is the probability that a team has fewer than 2 bilingual students? [T /2]