Question

A customer service center in Gary, Indiana receives, on average, 3.5 telephone calls per minute. If the distribution of calls is Poisson, what is the probability of receiving more than 4 calls during a particular minute? Do not round intermediate calculations. Round your final answer to four decimals. Format for probabilities: 0.0000

Answer 1

Solution :

Given that ,

mean = = 3.5

Using poisson probability formula,

P(X = x) = (e^- * ^x ) / x!

P(X > 4) = 1 - P(x 4)

= 1 - [P(x = 0)+ P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4)]

= 1 - [(e^-3.5 * 3.5⁰⁾ / 0! +  (e^-3.5 * 3.5¹⁾ / 1! +  (e^-3.5 * 3.5²⁾ / 2! +  (e^-3.5 * 3.5³⁾ / 3! +  (e^-3.5 * 3.5⁴⁾ / 4! ]

= 1 - 0.7254

= 0.2746

Probability = 0.2746