Find the indicated probabilities using the geometric distrib

Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine if the events are unusual. If convenient, use the appropriate probability table or technology to find the probabilities. Fifty-four percent of adults say that they have cheated on a test or exam before. You randomly select eighteight adults. Find the probability that the number of adults who say that they have cheated on a test or exam before is (a) exactly four, (b) more than two, and (c) at most five.

(a)P(4)=

Solution

i) Poisson distribution

As mean = 54% for 88 mean = 47.52

P(4) = 4.894x10^-16

P(>2) = 1

c) P(<=5) = 5.184x10^-15

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ii) Binomial:

p =0.54 q =046 n =88

P(4) = <0.00001

b) P(X>2) = 0.99999

c) P(X<=5) <0.00001

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Geometric distribution:

a) 0.068684

b) 1-P(0)-P(1) =1-0.4752 = 0.5148

c) P(<=5) = 0,4752+0.2494+0.1309+0.0687+0.0360

= 0.9602