177. In a group of 15 health insurance policyholders diagnosed with cancer, each policyholder
has probability 0.90 of receiving radiation and probability 0.40 of receiving
chemotherapy. Radiation and chemotherapy treatments are independent events for each
policyholder, and the treatments of different policyholders are mutually independent.
The policyholders in this group all have the same health insurance that pays 2 for
radiation treatment and 3 for chemotherapy treatment.
Calculate the variance of the total amount the insurance company pays for the radiation
and chemotherapy treatments for these 15 policyholders.
(A) 13.5
(B) 37.8
(C) 108.0
(D) 202.5
(E) 567.0
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