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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 and standard deviation
, the zscore of a measure X is given by
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
They have a standard deviation of standard deviation of 29 lb, so .
We have a sample of 8 adults, so we have to find the standard deviation of the sample to use in the place of in the Z score formula.
Find the probability that it is overloaded because they have a mean weight greater than 162 lb, so
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.
Answer:
The volume of pyramid B is 81 cubic units
Step-by-step explanation:
Given
<u>Pyramid A</u>
-- base sides
-- Volume
<u>Pyramid B</u>
--- base sides
Required
Determine the volume of pyramid B <em>[Missing from the question]</em>
From the question, we understand that both pyramids are equilateral triangular pyramids.
The volume is calculated as:
Where B represents the area of the base equilateral triangle, and it is calculated as:
Where s represents the side lengths
First, we calculate the height of pyramid A
For Pyramid A, the base area is:
The height is calculated from:
This gives:
Make h the subject
To calculate the volume of pyramid B, we make use of:
Since the heights of both pyramids are the same, we can make use of:
The base area B, is then calculated as:
Where
So:
So:
Where
and