MATH SOLVE

3 months ago

Q:
# An elevator has a placard stating that the maximum capacity is 1296 lb long dash — 8 passengers. So, 8 adult male passengers can have a mean weight of up to 1296 divided by 8 equals 162 pounds. 1296/8=162 pounds. If the elevator is loaded with 8 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 162 lb. (Assume that weights of males are normally distributed with a mean of 170 lb and a standard deviation of 29 lb.) Does this elevator appear to be safe?

Accepted Solution

A:

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.