Please show all your work THANK YOU The number of telephone

Please show all your work. THANK YOU

The number of telephone calls coming into a buisnes\'s switchboard averages 4 calls per minute. Let x be the number of calls received. This is Poisson....

A. Find P(x=0)

B. Find the probability there will be at lease 1 call in a given 1 minute period

C. Find the probability there will be exactly 4 calls in a given 1 minute period

Solution

Possion Distribution
PMF of P.D is = f ( k ) = e- x / x!
Where   
= parameter of the distribution.
x = is the number of independent trials

a)
P( X = 0 ) = e ^-4 * 4^0 / 0! = 0.0183

b)
P( X < 1) = P(X=0)   
= e^-4 * 0 ^ 0 / 0!   
= 0.0183

P( X > = 1 ) = 1 - P (X < 1) = 0.9817

c)
P( X = 4 ) = e ^-4 * 4^4 / 4! = 0.1954