Suppose Metro by T-Mobile wants to offer a simple extended warranty plan. If your phone is damaged, they will repair it for up to $50. If you lose or destroy your phone, they will give you a $200 voucher towards a new phone. The company believes that 5% of customers will need the replacement voucher and 10% will request a repair. What is the standard deviation?

45

Step-by-step explanation:

Given that :

Voucher awarded (x) :

Repair = $50

Lose or destroy = $200

P(x):

Replacement voucher = 5%

Repair voucher = 10%

X 50 200

P(x) 0.1 0.05

Expected variance Var(X) :

ΣX²p(x) - E(x) ;

E(x) = Σx*p(x) = (50*0.1) + (200*0.05) = 15

ΣX²p(x) = Σ[(50^2 * 0. 1) + (200^2 * 0.05)] = 250 + 2000 = 2250

Var(X) = 2250 - 15^2 = 2025

Standard deviation = √Var(x)

Standard deviation = √2025

Standard deviation = $45