Models of the pricing of stock options often make the assumption of a normal distribution. An analyst believes that the price of an Initech stock option varies from day to day according to normal distribution with mean $9.22 and unknown standard deviation.
a.The analyst also believes that 77% of the time the price of the option is greater than $7.00. Find the standard deviation of the price of the option.
b. Find the proportion of days when the price of the option is greater than $10.00?
c. Following the famous "buy low, sell high" principle, the analyst recommends buying Initech stock option if the price falls into the lowest 14% of the price distribution, and selling if the price rises into the highest 9% of the distribution. Mr. Statman doesn't know much about history, doesn't know much about biology, doesn't know much about statistics, but he does want to be rich someday. Help Mr. Statman find the price below which he should buy Initech stock option and the price above which he should sell.