Respuesta :
Answer:
There is a 25.14% probability that the order will not be met during a month.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean \mu 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. Subtracting 1 by the pvalue, we This p-value is the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 4500, \sigma = 900[/tex].
The order will not be met if [tex]X > 6000[/tex]. So we find the pvalue of Z when [tex]X = 6000[/tex], and subtract 1 by this value.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{6000 - 4500}{900}[/tex]
[tex]Z = 1.67[/tex]
[tex]Z = 1.67[/tex] has a pvalue of 0.7486.
So there is a 1 - 0.7486 = 0.2514 = 25.14% probability that the order will not be met during a month.
