Your boss asks you to use your new probability skills to build a model of the nu

Question

Your boss asks you to use your new probability skills to build a model of the number of drive-up customers served at the main branch per day, and the purpose of this model is to help determine the number of staff members assigned to the drive-up window at the bank. You interview the staff members who have experience with drive-up banking, and they tell you that the most drive-up customers served per day is about 80 people and that the smallest number of drive-up customers is about 10 per day. Further, the senior teller at the bank tells you that the number of daily customers is evenly distributed between these high and low values. Based on this information, which probability model would be a good candidate for the number of drive-up customers per day? What is the mean and variance of this model?

Explanation / Answer

Suppose X is a random variable which takes the values of total customers arrive per day.

It is given that the number of customers is evenly distributed between these high and low values.

That is the probability of X (number of customers arrive per day) is equal from low to high values.

Also it is given that low value = 10 and high value = 80

Therefore the best probability model is discrete uniform with parameters [a, b]. = [10, 80]

P(x) = 1/(b - a +1) = 1/ N = 1/71 X = 10, 11, ...80.

Mean of discrete uniform with parameters [a, b] = (a + b )/2 = 45

variance of discrete uniform with parameters [a, b] = {(b - a +1)^2 - 1}/12 = (71^2 -1)/12 = (5041 - 1)/12 = 5040/12

Variance = 5040/12 = 420

Standard deviation = SQRT(420) =20.4939

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.