Use a Bernoulli Single-Server Queuing Process with limited capacity for this pro

Question

Use a Bernoulli Single-Server Queuing Process with limited capacity for this problem. A phone line allows an employee to talk with one customer and have another customer on hold. On average the phone receives 15 calls per hour and each call typically lasts 2 minutes. (a) Using a frame size of 30 seconds, set up the transition probability matrix. (b) What proportion of time is a customer on hold long-term? People's weights are (approximately) normally distributed. Suppose the average weight in a certain population is 170 pounds with a standard deviation of 20 pounds. What is the probability that a random group of 10 people from this population has a total weight greater than 1500 pounds? Compute the probability that 350 gigabytes of disk space is sufficient to store 100 digital files, assuming the average size of a file is 3.3 gigabytes with a standard deviation of 1.5 gigabytes.

Explanation / Answer

question 2

mean = 170 sd = 20 , n= 10 and we need to find , 10 people total weight is 1500 so avg is 1500/10 = 150

we must calculate that P(X>150) , please keep the z tables handy for this.

so we convert this into a z score as

Z = (X-Mean)/(SD/sqrt(n))

(150-170)/(20) = -1

so P(Z>-1)

P ( Z>1 )=P ( Z<1 )=0.8413

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