In: Math
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?
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