Suppose the X is a Poissonrandom variablewith lambda = 6.

a) Compute the exact probabilitythat X is less than 4

b) Approximate the probability that X is less than 4 and compare to a)

c) Approximate the probability that 8<X<12

Please see the attachment.

Normal Approximations to the Poisson distribution

Suppose the X is a Poisson random variable with lambda = 6.

a) Compute the exact probability that X is less than 4

b) Approximate the probability that X is less than 4 and compare to a)

c) Approximate the probability that 8<X<12

Answer

The probability density function of Poisson variable with =6 is given …

Step by step method for computing probability for Poison distribution based on normal approximation is give in the answer.