Respuesta :
Answer:
There is a 78.81% probability that they will run out of raw material.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X. The sum of the probabilities is decimal 1. So 1-pvalue is the probability that the value of the measure is larger than X.
In this problem
The demand for the polymer is forecasted to be normally distributed with a mean of 250 gallons and a standard deviation of 125 gallons. So [tex]\mu = 250, \sigma = 125[/tex].
Suppose Goop purchases 150 gallons of raw material. What is the probability that they will run out of raw material? That is [tex]P(X > 150)[/tex].
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{150 - 250}{125}[/tex]
[tex]Z = -0.8[/tex]
[tex]Z = -0.8[/tex] has a pvalue of 0.2119. This means that [tex]P(X \leq 150) = 0.2119[/tex]
Also
[tex]P(X \leq 150) + P(X > 150) = 1[/tex]
[tex]P(X > 150) = 1 - 0.2119 = 0.7881[/tex]
There is a 78.81% probability that they will run out of raw material.
