Question

Give a distribution that might best model each of the following situations:

a) The processing time on a computer chip insertion machine

b) The time that it takes a person to order from a fast food restaurant

c) The time that it takes for a light-bulb to burn out

d) The number of defects on a computer chip wafer

e) The number of phone calls until a successful sale

Answer 1

a) The processing time on a computer chip insertion machine follows Normal distribution.

b) The time that it takes a person to order from a fast food restaurant follows Poisson and exponential distribution.

In service distribution Poisson and exponential are directly related to each other.If the number of arrivals follow Poisson distribution,it turns out the time between successive arrivals follows an Exponential distribution.

c) The time that it takes for a light-bulb to burn out.

Suppose that a new bulb is put in at time 0.it will last for an amount of time t.Using the lack of memory property of the Exponential distrubution,it follows that the amount of time until the next inspection will have an exponential distribution withe same rate.The bulb is then replaced and the cycle starts again so we have an alternating renewal process..So the time that it takes for s light bulb follows renewal distribution.

d) The number of defects on a computer chip wafer.

The number of defects per wafer found to follows Binomial distribution if the manufacturing process is stable.

e) The number of phone calls until a successful sale follows Geometric distribution

The random variable that counts the number of independent Bernoulli trials necessary to obtain the first success is called a Geometric Random variable.