Worksheet 07 - Binomial and Poisson Distributions PDF

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Worksheet for seminar 7 Binomial and Poisson Distributions...

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MA0371 – Statistics

Worksheet 07

Binomial and Poisson Distributions 1. A computer program can process a string of 10 words. To test this program you have created a database of 50 different words. How many test strings of 10 unique words can you generate from the database? 2. You are throwing a party, but because of the size of your room you can only invite 10 of your 30 best friends. How many sets of 10 friends do you have to choose from? 3. A production line is known to produce 10% defective items out of its total production. If 5 items are selected at random for inspection, what is the probability that only one of these will be defective? 4. A salesman makes four calls in a day. At each call there is a probability of 1/5 of making a sale. What is the probability that the salesman will make at most one sale in the day? 5. Which of the following can be modelled with a binomial distribution? In those cases where it is suitable, define an appropriate random variable and values for n and p. a) The number of girls in a class of 20 children b) The number of sixes when 5 dice are thrown c) The number of throws of a die needed before you throw a six. d) The number of tosses before a tail results from a coin that is biased so that a head is twice as likely as a tail. e) The number of tails in ten tosses of a coin that is biased so that a head is twice as likely as a tail. f) The number of blue marbles when six marbles are taken without replacement from a bag containing 10 blue marbles and 20 white marbles. g) The number of blue marbles when six marbles are taken with replacement from a bag containing 10 blue marbles and 20 white marbles.

6. The random variable a)

P ( X=4)

7. The random variable a) b)

P(Y ≤6) P (Y < 6 )

X B (10,0.3) . Find: b)

P(X 4)

1 Y B(15, ) . Find: 4 c) d)

P(Y =6) P(6 ≤ Y ≤ 10)

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MA0371 – Statistics

Worksheet 07

8. A data processing agency employs temporary data entry operators to key data onto computer databases, and estimates that 15% of data entries contain an error. If a new data entry operator makes 20 data entries, what is the probability that: a) b) c) d) e)

less than 6 contain an error? at least 8 contain an error? exactly 2 will contain an error? none will contain an error? from 2 to 6 inclusive will contain an error?

9. In an inspection scheme a sample of 20 items is selected at random from a very large batch and the number of defective items is recorded. If this is more than two the batch is rejected; if it is less than two the batch is accepted. If the number of defective items is exactly two a further sample of 10 items is taken and the batch is rejected if there is more than one defective in the second sample but accepted otherwise. If the proportion of defective items in the batch is 1%, determine the probability that; a) the batch is accepted as a result of inspection of the first batch. b) a further sample has to be taken and the second batch is accepted. c) a further sample has to be taken and the second batch is rejected. 10. If one in twenty people are left-handed, what size sample should be taken to ensure that the expected number of left-handed people in the sample is three? 11. If a) b) c)

X B ( 10,0.4 ) Find the mean μ Find the standard deviation σ Evaluate P(μ−σ...