finding probability of account balance and determining the account balance

Question

The account balances for customers holding a particular type of a bank account with National Bank are normally distributed with mean=205,000.00 and a standard deviation=25,000.00

1. Determine the probability that the account balance for a particular customer with an account of this type is between 200,000.00 and 250,000.00

2. The bank decides to grade such customers by account balances. It has decided that the lowest 33% should be graded as Bronze, the highest 20.9% graded as Gold, the remaining Silver. Determine the account balance above which Gold customers fall 

Answer 1

If 25,000 is 1 standard deviation (1 sigma), then 50,000 is 2 sigma

 

Look at the Gaussian curve here:

http://hyperphysics.phy-astr.gsu.edu/hbase/math/gaufcn.html

 

EDIT--See my note below about an error