Question

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Beer drinkers order an average of 50 pitchers of beer per hour at Nick's Pub in...

Beer drinkers order an average of 50 pitchers of beer per hour at Nick's Pub in

Bloomington, Indiana. Answer the following questions:

• What is the probability that at least 100 pitchers are ordered in a three-hour period?

• What is the chance that the time between ordered pitchers will be 45 seconds or less?

B.An average of 100 customers arrive each hour at the Central Forest Coffee Shop. What

is the probability that at least 170 customers arrive in a two-hour period?

Solutions

Expert Solution

Let X denotes the number of pitchers ordered in a three-hour period.

X ~ Poisson(50*3) or X~ Poisson(150)

The probability mass function of X is

The probability that at least 100 pitchers are ordered in a three-hour period

Let Y denotes the time between ordered pitchers.

Y follows Exponential distribution with mean = 50/60 = 0.833333

Now,

The probability that the time between ordered pitchers will be 45 seconds (or 45/60 = 3/4 = 0.75 minutes) or less

B) Let X denotes the number of customers arrived in a two-hour period.

X ~ Poisson(100*2) or X ~ Poisson(200)

The probability mass function of X is

Now,

The probability that at least 170 customers arrive in a two-hour period

milcah answered 10 months ago

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