Respuesta :
Answer:
There is a 98.26% probability that it is overloaded.
This elevator does not appear to be safe.
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. 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:
Assume that weights of males are normally distributed with a mean of 170 lb, so [tex]\mu = 170[/tex]
They have a standard deviation of standard deviation of 29 lb, so [tex]\sigma = 29[/tex].
We have a sample of 8 adults, so we have to find the standard deviation of the sample to use in the place of [tex]\sigma[/tex] in the Z score formula.
[tex]s = \frac{\sigma}{8} = \frac{29}{8} = 3.625[/tex]
Find the probability that it is overloaded because they have a mean weight greater than 162 lb, so [tex]X = 162[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{162 - 170}{3.625}[/tex]
[tex]Z = -2.21[/tex]
[tex]Z = -2.21[/tex] has a pvalue 0.0174.
So, there is a 1-0.0174 = 0.9826 = 98.26% probability that it is overloaded.
Any probability that is above 95% is considerer unusually high. So, this elevator does not appear to be safe, since there is a 98.26% probability that it is overloaded.