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1) Suppose that a student pilot passes a written test for a private pilot\'s lic

ID: 3128558 • Letter: 1

Question

1) Suppose that a student pilot passes a written test for a private pilot's license is .07.Find the probability that the student will pass the test a) on the third try b) before the 4th try. c) What is the expected number of attempts the student has to take to pass the test? 2) Suppose that the number of tornadoes observed in a particular region during a on-year period has a Poisson distribution with = .8. a) Find the probability that there will be at most 5 tornadoes in a 1-year period in that region. b) Find the probability that the number of tornadoes observed in a 1-year period in that region is between 6 and 9 both inclusive. c) What is the probability that the number of tornadoes exceeds the expected number by more than one standard deviation?

Explanation / Answer

the probability that the student will pass the test

a) on the third try =P(fail in first two and pass in third)

=0.93^2 (0.07)

=0.0563

b) before the 4th try=P( passes in first or second or third)

= 0.07(1+0.93+0.93^2)

= 0.2004

c) E(X) = Mean of geometric distribution = 1/p = 14.2857

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Y no of tornadoes isPoisson with mean = 0.8

P(Y<=5) = 0.9998

P(6<y<9) = P(Y<9)-P(Y<6)

= 0.99999-0.9998

=0.000019

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E(Y) = 0.8 and std dev = 0.8944

Y should lie between (0.8944, 1.6944)

P(Y = 1) = 0.3595