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McMingMing
06.01.2021 •
Mathematics
What has the same solution as 8x + 3y = 5
4x + 2y = 3
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Ответ:
The weights of the package follows a probability density function
The mean is 4.31 and the variance is 51.42, respectively.The average cost of shipping a package is $10.78The probability a package weighs over 59 pounds is 0.0027The probability density function is given as:
(a) The mean and the variance
The mean is calculated as:
So, we have:
Rewrite as:
Integrate
Expand
The variance is calculated as:
Where:
So, we have:
Rewrite as:
Integrate
Expand
So, we have:
Hence, the mean is 4.31 and the variance is 51.42, respectively.
(b) The average cost of shipping a package
In (a), we have:
So, the average cost of shipping a package is:
Hence, the average cost of shipping a package is $10.78
(c) The probability a package weighs over 59 pounds
This is represented as: P(x > 59)
So, we have:
So, we have:
Rewrite as:
Integrate
Expand
Hence, the probability a package weighs over 59 pounds is 0.0027
Read more about probability density functions at:
link