Stat 211- Second Term 1429/1430H
Assignment . 4 Part I Assignment . 4 Part I Assignment . 4 Part I Assignment . 4 Part I
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1. Suppose 20 percent of the items produced by a factory are defective. Suppose 4 items are chosen at random.
i) Name of distribution.
ii) Find the probability that:
a) 2 are defective.
b) None is defective.
2. A student takes an 18-question multiple-choice exam, with 4 choices per question.
Suppose one of the choices is obviously incorrect, and the student make an
"educated" guess of the remaining choices.
i) Name of distribution.
ii) Find the expected number and standard deviation of correct answers.
iii) Find MGF, and FMGF.
3. A class has 18 boys and 12 girls. If the teacher randomly selected a group of 15 student to represent the class in a competition,
i) Name of distribution.
ii) determine the following:
a) The probability that 8 members of the group are girls b) The expected number of boys in the group.
4. A fair die is rolled repeatedly until a 6 appears.
i) Name of distribution.
ii) What is the probability that the experiment stops at the fourth roll?
iii) Given that the experiment stops at the third roll, what is the probability the sum of all the three rolls is at least 12?
iv) Find E(x), Var(x), MGF, and FMGF.
5. Twenty percent of the population of a particular city wear glasses. If you randomly stop people from that city. Determine the following probabilities:
a) It takes exactly 10 tries to get a person who wears glasses.
b) It takes at least 10 tries to get a person who wears glasses.
c) It takes exactly 10 tries to get the third person who wears glasses.
d) It takes at least 10 tries to get the third person who wears glasses.
Stat 211- Second Term 1429/1430H
Assignment . 4 Part I Assignment . 4 Part I Assignment . 4 Part I Assignment . 4 Part I
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6. The number of phone calls that arrive at a secretary's desk has a Poisson distribution with a mean of 4 per hour.
a) What is the probability that no phone calls arrive in a given hour?
b) What is the probability that more than 2 calls arrive within a given hour?
c) Find , E(x), Var(x), MGF, and FMGF.
7. If X has a Poisson distribution and P(X=2)=(2/3)P(X=1), findP(X=3), and P( X−2 >1).
