An entrepreneur in a developing country owns 10 food carts. He has ten employees
ID: 3150392 • Letter: A
Question
An entrepreneur in a developing country owns 10 food carts. He has ten employees to work with these food carts. Let Xi be a random variable representing revenue from cart i (on a particular day), i = 1,..., 10. Xi is approximately normally distributed with mean $35, and variance 64 (squared dollars). Revenues of the different carts are independent.
What is the probability that cart i will generate revenue less than $30 on a particular day? In this question the cumulative distribution function of the standard normal random variable is denoted by F(.).
Explanation / Answer
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 30
u = mean = 35
s = standard deviation = 8
Thus,
z = (x - u) / s = -0.625
Thus, using a table/technology, the left tailed area of this is
F(30) = P(z < -0.625 ) = 0.265985529 [ANSWER]