Customers in a Bank In the Ames International Campus Bank (open 24h every day) 5 customers arrive on average during an hour. Ans
wer the following questions. First write down the problem in terms of some random variables and write down what distribution assumptions you make about these random variables. (a) What is the probability that during an hour no customer arrives? (b) What is the probability that during an hour, 7 or more customers arrive? (c) What is the probability that there's more than 30 minutes between the 2nd and 3rd customer of the day? (d) What is the probability that you have to wait less than an hour for seven customers to arrive? (e) How many minutes do you expect to wait until the 12th customer arrives? (f) How many minutes do you expect to wait on average between arrivals?
1 answer:
You might be interested in
Answer:
a) X ~
b) μ = 100/3
c)
d) A battery is expected to last 100/3 months (33 months and 10 days approximately).
e) For seven batteries, i would expect them to last 700/3 months (approximately 19 years, 5 months and 10 days).
Step-by-step explanation:
a) The life of a battery is usually modeled with an exponential distribution X ~
b) The mean of X is μ = 1/0.03 = 100/3
c) The standard deviation is
d) The expected value of the bateery life is equal to its mean, hence it is 100/3 months.
e) The expected value of 7 (independent) batteries is the sum of the expected values of each one, hence it is 7*100/3 = 700/3 months.