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Sagot :
Answer:
The standard deviation is 17.5
Step-by-step explanation:
Let S be the sum of X and Y
S = X + Y
So we want to calculate the standard deviation of S
The standard deviation of S will be the square root of the sum of the variances of X and Y
Kindly recall that variance is the square of standard deviation
The variance of X will be 15^2 = 225
The variance of Y will be 9^2 = 81
So the standard deviation of the sum will be
√(81 + 225)
= √(306)
= 17.5
The standard deviation of X + Y is 17.5
The given parameters are:
[tex]\bar x =120[/tex] --- the mean of X
[tex]\sigma_x =15[/tex] -- the standard deviation of X
[tex]\bar y = 100[/tex] --- the mean of Y
[tex]\sigma_y = 9[/tex] --- the standard deviation of Y
The standard deviation of X + Y is then calculated as:
[tex]\sigma_{x +y} = \sqrt{\sigma_x^2 + \sigma_y^2}[/tex]
This gives
[tex]\sigma_{x +y} = \sqrt{15^2 + 9^2}[/tex]
Evaluate the exponents
[tex]\sigma_{x +y} = \sqrt{225 + 81}[/tex]
[tex]\sigma_{x +y} = \sqrt{306}[/tex]
Take the square root of 306
[tex]\sigma_{x +y} = 17.5[/tex]
Hence, the standard deviation of X + Y is 17.5
Read more about standard deviation at:
https://brainly.com/question/475676
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