Use Bernoulli Binomial Geometric Poission or other type of s

Use Bernoulli, Binomial, Geometric, Poission, or other type of special distribution

(1) Ten percent of computer parts produced by a certain supplier are defective. What is the probability that a sample of 10 parts contains more than 3 defective ones? (2) On the average, two tornadoes hit major U.S. metropolitan areas every year. What is the probability that more than five tornadoes occur in major U.S. metropolitan areas next year?

Solution

(1) Given X follows Binomial distribution with n=10 and p=0.1

P(X=x)=10Cx*(0.1^x)*(0.9^(10-x)) for x=0,1,2,...,10

So the probability is

P(X>3) = 1-P(X=0)-P(X=1)-P(X=2)-P(X=3)

=1-10C0*(0.1^0)*(0.9^(10-0))-...-10C3*(0.1^3)*(0.9^(10-3))

= 0.0127952

---------------------------------------------------------------------------------------------------------

(2)Given X follows Poisson distribution with mean=2

P(X=x)=(2^x)*exp(-2)/x!

So the probability is

P(X>5) =1-P(X=0)-P(X=1)-...-P(X=5)

=1-(2^0)*exp(-2)/1-...-(2^5)*exp(-2)/5!

=0.01656361