Question

A trash disposal company has determined that the amount of trash that a local city's daily trash production follows a normal distribution. The mean amount of trash the city makes each day is 101.3 tons, and the standard deviation is 18.5 tons. The company wants the capacity of its truck fleet to be large enough to handle the city's production 97.5% of the time. How many tons of trash is that?

HINT: use the NORM.INV function.

a	137.6
b	138.2
c	141.3
d	142.4

Answer 1

Solution :

Given that,  

mean = $\mu$ = 101.3

standard deviation = $\sigma$ = 18.5

Using standard normal table ,

P(Z < z) = 97.5%

P(Z < 1.96) = 0.975

z = 1.96

Using z-score formula,

x = z * $\sigma$ + $\mu$

x = 1.96 * 18.5 + 101.3 = 137.6

137.6 tons of trash

option a. is correct