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
