Respuesta :
Answer:
This means that there is a 1-0.3594 = 0.6406 = 64.06% probability that the elevator is overloaded. This a good chance that the elevator's limit weight will be exceeded. So, 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 163 lb and a standard deviation of 29 lb.
This means that [tex]\mu = 163, \sigma = 29[/tex].
We have a sample of 12 adults, and we want to calculate the zscore of THE SAMPLE'S AVERAGE so we need to find the standard deviation of the sample. This is
[tex]s = \frac{\sigma}{\sqrt{12}} = 8.37[/tex]
Find the probability that it is overloaded because they have a mean weight greater than 160.
This is 1 subtracted by the pvalue of Z when [tex]X = 160[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{160 - 163}{8.37}[/tex]
[tex]Z = -0.36[/tex]
[tex]Z = -0.36[/tex] has a pvalue of 0.3594.
This means that there is a 1-0.3594 = 0.6406 = 64.06% probability that the elevator is overloaded. This a good chance that the elevator's limit weight will be exceeded. So, this elevator does not appear to be safe.
