Models of the pricing of stock options often make the assumption of a normal dis

Question

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 $ 9.23 and unknown standard deviation. (As usual, for this question you can enter your answer in decimals as well as fraction.)

1.Find the proportion of days when the price of the option is greater than $ 9.93 ? (Note : for this question and the next two parts you can write your answer in terms of functions (or codes) in the statistical software R. e,g the functions pnorm(x), qnorm(x), exp(x) etc. Syntax of R must be strictly followed. It is probably a good idea to run the code in R before entering as your answer will be evaluated by R. Traditional numerical (both decimal and fractions) answers are also accepted. )

Explanation / Answer

proportion of days when the price of the option is greater than $ 9.93

Z= (9.93-9.23)/3

=0.23

probability at Z =0.23

=0.59059

=59.05%

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