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Korvikt [17]
3 years ago
5

Assume X and Y are indepndent. Assume that X has mean 10 and standard deviation 8. Assume Y has mean 12 and standard deviation 6

. What is the standard deviation of the variable Z = X + Y. a. 8 b. 6 c. 10 d. 12
Computers and Technology
1 answer:
Vitek1552 [10]3 years ago
6 0

Answer:

\sigma_z = 10

Explanation:

Given

\bar x = 10

\sigma_x = 8

\bar y = 12

\sigma_y = 6

z = x + y

Required

\sigma_z

This is calculated as:

\sigma_z = \sqrt{Var(x) + Var(y)}

Calculate Var(x)

We have:

Var(x) = \sigma_x^2

Var(x) = 8^2

Var(x) = 64

Calculate Var(y)

We have:

Var(y) = \sigma_y^2

Var(y) = 6^2

Var(y) = 36

So, we have:

\sigma_z = \sqrt{Var(x) + Var(y)}

\sigma_z = \sqrt{64 + 36}

\sigma_z = \sqrt{100}

\sigma_z = 10

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