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Q1. Customers arrive to a bank. The chance to leave without receiving a service for every...

Q1. Customers arrive to a bank. The chance to leave without receiving a service for every customer is 0.05. Answer the following questions: [Hint this is Bernoulli trial with a probability of success (leaving without receiving a service) is 0.05 and probability of failure (leaving after receiving a service) is 0.95]

What is the probability that no customer will leave without receiving a service for the next 10 customers?

What is the probability of that less than 3 customers will leave without receiving a service for the next 10 customers?

What is the expected number of customers (mean) leave without receiving a service for the first 100 arrivals?

What is the probability that the first customer leaves without receiving a service comes at the customer number 100?

What is the probability that the third customer leave without receiving a service comes at customer number 100?

What is the expected number of customer to see the first leave without receiving a service?

What is the variance for the number of trials before seeing the first leave without receiving a service?

Math   Statistics-And-Probability   
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Answer #1

1) probability that no customer will leave without receiving a service for the next 10 customers=(1-0.05)10 =0.5987

2) probability of that less than 3 customers will leave without receiving a service for the next 10 customers =P(X<3)

= =0.9885

3)

expected number of customers (mean) leave without receiving a service for the first 100 arrivals=np=100*0.05 =5

4)

probability that the first customer leaves without receiving a service comes at the customer number 100 =(0.95)99*0.05=0.000312

5)

probability that the third customer leave without receiving a service comes at customer number 100
=99C2(0.05)3(0.95)97 =0.004187

6)

expected number of customer to see the first leave without receiving a service=1/p=1/0.05 =20

variance for the number of trials before seeing the first leave without receiving a service=(1-p)/p2 =380

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