A bank offers three different savings accounts: Type A that yields 10% interest,

Question

A bank offers three different savings accounts: Type A that yields 10% interest, Type B that yields 7% interest, and Type C that yields 12% interest over each year. The amounts invested in each account at the start of the year are independent and normally distributed random variables, with the following parameters (in millions):

Type µ

A 3.0 0.6

B 1.5 0.8

C 2.0 1.0

Assuming no other deposits or withdrawals are made, what is the 90th percentile of the distribution of the total amount of interest paid by the bank during the year (in millions)?

A. 0.831

B. 0.845

C. 0.947

D. 1.219

E. 1.268

Explanation / Answer

here total amount of interst X =(10A+7B+12C)/100

hence mean of X =(10*3+7*1.5+12*2)/100=0.645

and std deviaiton =(1/100)*((10*0.6)2+(7*0.8)2+(12*1)2)1/2 =0.1454

for 90th percentile ; z =1.2816

therefore coresponding value =mean +z*std deviation =0.645+1.2816*0.1454 =0.831

option A is correct

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