Question

Assume that you run a call center that receives an average of 3 calls per minute with a Poisson distribution. Use this information to answer questions 1 to 4.

1. What is the probability that the call center receives exactly 2 calls in the next minute? Use the formula and show your work.
2. What is the probability that the call center receives exactly 4 calls in the next minute?
3. What is the probability that the call center receives exactly one call in the next 20 seconds?
4. What is the probability that the call center receives 2 or more calls in the next 20 seconds?

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5. A particular industry has 15 companies. At the beginning of the year you picked ten of these companies at random and bought stock in these ten companies. During the year a total of 11 of the companies in the industry made a profit and 4 made a loss. What is the probability that exactly 7 of the companies you bought stock in made a profit during the year?

Answer 1

Ans:

average number of calls=3 calls per minute

P(x=k)=exp(-3)*(3^k/k!)

1)

P(x=2)=exp(-3)*(3^2/2!)=0.2240

2)

P(x=4)=exp(-3)*(3^4/4!)=0.1680

Now,

average number of calls in 20 sec=(3/60)*20=1

P(x=k)=exp(-1)*(1^k/k!)

3)

P(x=1)=exp(-1)*(1^1/1!)=0.3679

4)

P(x>=2)=1-P(x<=1)

=1-P(x=0)-P(x=1)

=1-exp(-1)*(1^0/0!)-exp(-1)*(1^1/1!)

=1-exp(-1)-exp(-1)

=0.2642