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A bank estimates that its profit next year is normally distributed with a mean of 0

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A bank estimates that its profit next year is normally distributed with a mean of 0.8% of assets and the standard deviation of 2% of assets. How much equity (as a percentage of assets) does the company need to be (a) 99% sure that it will have a positive equity at the end of the year and (b) 99.9% sure that it will have positive equity at the end of the year? Ignore taxes.

(a) The bank can be 99% certain that profit will better than 0.8−2.33×2 or -3.85% of assets. It therefore needs equity equal to 3.85% of assets to be 99% certain that it will have a positive equity at the year end.

(b) The bank can be 99.9% certain that profit will be greater than 0.8 − 3.09 × 2 or -5.38% of assets. It therefore needs equity equal to 5.38% of assets to be 99.9% certain that it will have a positive equity at the year end.