Problem : Fast Food Restaurant

A fast-food restaurant sells As and Bs. On a typical weekday the demand for As is normally distributed with mean 313 and standard deviation 57; the demand for Bs is normally distributed with mean 93 and standard deviation 22.

  1. How many As must the restaurant stock to be 98% sure of not running out of stock on a given day ?
qnorm(0.98,313,57)
## [1] 430.0637
  1. How many Bs must the restaurant stock to be 90% sure of not running out of stock on a given day ?
qnorm(0.9,93,22)
## [1] 121.1941
  1. If the restaurant stocks 450 As and 150 Bs for a given day, what is the probability that it will run out of stock for As or Bs (or both) that day? Assume that the demand for As and Bs are probabilistically independent.
p_s <- 1-pnorm(450,mean=313,sd=57)
p_w <- 1-pnorm(150,mean=93,sd=22)
p_s + p_w - p_s*p_w
## [1] 0.01286657