Advanced Placement (AP) High School

Find the standard deviation of the following R.V. Show all work...no calculator shortcuts...but then check with 1-var stats.



X 7 15 28
P(X) 0.2 0.49 ?
Round to FOUR decimal places.

Answers

Answer 1

Answer:

7.6997

Explanation:

Given :

X : ____7 ____ 15 ____ 28

P(X) __0.2 ___0.49 ____?

ΣP(x) = 1

0.2 + 0.49 + a = 1

a = 1 - 0.69

a = 0.31

Standard deviation = sqrt(Variance(x))

Variance = Var(X) = Σx²p(x) - E(x)²

E(x) = Σx*p(x) = (7*0.2) + (15*0.49) + (28*0.31) =

E(x) = 17.43

Σx²p(x) = (7^2 * 0.2) + (15^2 * 0.49) + (28^2 * 0.31) = 363.09

Var(X) = Σx²p(x) - E(x)²

Var(X) = 363.09 - 17.43^2

Var(X) = 363.09 - 303.8049

Var(X) = 59.2851

Standard deviation = sqrt(59.2851)

Standard deviation = 7.6996818

= 7.6997

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