Regulators calculate that DLC bank (see Section 2.2) will report a profit that

Regulators calculate that DLC bank (see Section 2.2) will report a profit that is normally distributed with a mean of $0.6 million and a standard deviation of
$2.0 million. How much equity capital in addition to that in Table 2.2 should regulators require for there to be 99.9% chance of the capital not being wiped
out by losses?

Table 2.2:

Summary of Balance Sheet for DLC at End of 2012 ($millions)

Assets:

Cash 5

Marketable Securities 10

Loans 80

Fixed Assets 5

Total 100

Liabilities and Net Worth:

Deposits 90

Subordinated Long-Term Debt 5

Equity Capital 5

Total 100

Table 2.3: Summary Income Statement for DLC in 2012 ($ millions)

Net interest income 3.00

Loan Losses (0.80)

Non-interest income 0.90

Non-interest expense (2.50)

Pre-tax operating income 0.60