Answer:
z= - 0.58
Step-by-step explanation:
Normal Distribution
Also known as Gauss Distribution is one of the most used continuous probability distribution to characterize random events. The standard Normal Distribution is a special case of the general distribution where the mean [tex]\mu[/tex] is zero and the standard deviation [tex]\sigma[/tex] is 1. The values of the normal distribution cannot be obtained by simple calculations, they are instead given as tables or functions integrated with tools like Excel.
The entry for standard normal distribution is a parameter called z-score, who is zero in the very center of the bell curve, for a cummulative probability of 0.5. For z less than zero, the cummulative probability is less than 0.5, for z greater than zero, the cummulative probability is greater than 0.5. It's written as p(z).
When we are given the cummulative probability, we need to use the inverse normal distribution function [tex]p^{-1}[/tex] to find z.
We are given the value of the probability of the left tail of the bell curve, i.e. the cummulative probability
p(z)=0.281. It clearly corresponds to a negative value of z
We'll use the inverse z-scrore function of MS Excel (NORM.INV), which only parameter is p to find z
z=NORM.INV(0.281)
z=-0.58
