A pyramid-shaped hip roof is a good choice for a house in an area with many hurricanes. What is the volume of the roof to the ne
arest tenth of a foot? What is the volume of the entire house, including the roof?
1 answer:
The volume of the roof is 10667 cube feet and the volume of the entire house, including the roof, is 58667 cube feet.
<h3>How to find the volume of the composite figures?</h3>To find the volume of the composite figures, follow the steps listed below:,
- Separate the figure.
- Calculate the volume of each figure by which the composite figure is made of.
- Add the volume of all the individual figures to get the total volume of composite figures.
A pyramid-shaped hip roof is a good choice for a house in an area with many hurricanes. The volume of the roof is:
The volume of the room is:
V=length x width x height
V=40 x 40 x 30
V=48000 ft³
The volume of the entire house, including the roof, is,
V=10667+48000
V=58667 ft³
Thus, the volume of the roof is 10667 cube feet and the volume of the entire house, including the roof, is 58667 cube feet.
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Answer:
x = 128.472
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. 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, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The number of diners each day has a mean of 107 and a standard deviation of 60.
This means that
Distribution of the daily average:
Over a month of 30 days, so
The probability that a daily average over a given month is greater than x is 2.5%. Calculate x.
This is X when Z has a p-value of 1 - 0.025 = 0.975, so X when Z = 1.96. Then
By the Central Limit Theorem
So x = 128.472