LUUVpla3831811ditcontentrid23001326 1HW 624pdf ISYE335 Homew

LUUV)pla-3831811-dit-content-rid-23001326 1/HW 624.pdf ISYE335 Homework #4 (Due March 4th, 2015) Spring 2015 4. Suppose that X is a binomial random variable with n 200 and p 0.4. (a) Approximate the probability that X is less than or equal to 70. (b) Approximate the probability that Xis greater than 70 and less than 90. (c) Approximate the probability that X 80. 5. Suppose that X is a Poisson random variable with (a) Compute the exact probability that X is less than 4. (b) Approximate the probability that Xis less than 4 and com- pare to the result in part (a). (c) Approximate the probability that 8

Solution

x binomial with p = 0.4 and n =200

We calculate binomial probability table for calculating all of these

a) P(X<=70) =0.0844

b) P(70

= 0.8504

c) P(x=80) = 0.0575

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5) Poisson variable with mean =6

a) P(X<4)=0.1512

b) P(X<=4)=0.2850

c) P(8