SPlease provide solutions to the following Questions and show all necessary work

Question

SPlease provide solutions to the following Questions and show all necessary work. Feel free to use R or any statistical programming to answer the problem.

(Surgery)The probability for a complication after a particular type of surgery is P = 0:005. (a) Find the probability that there will be at least one complication in 100 of such surgeries. (b) Find the average number of complications after 100 surgeries. (c) Find the probability that there will be at least one complication after 1000 surgeries. (hint: use a poisson approximation)

Explanation / Answer

a) probability that there will be atleast one complication in 100 such surgeries =1-P(none complication)

=1-(1-0.005)100 =0.3942

B)average number of complications =np =100*0.005=0.5

c)

average number of complications =

probability =1-P( 0 complications)= 1-e-t =1-e-0.005*100 =0.3935

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