Question

For 300 trading​ days, the daily closing price of a stock​ (in $) is well modeled by a Normal model with mean ​$197.89 and standard deviation ​$7.17. According to this​ model, what is the probability that on a randomly selected day in this period the stock price closed as follows. ​a) above ​$205.06​? ​b) below ​$212.23​? ​c) between ​$183.55 and ​$212.23​? ​d) Which would be more​ unusual, a day on which the stock price closed above ​$210 or below ​$180​?

Answer 1

Mean = = 197.89

Standard deviation = = 7.17

a) P(X > 205.06)

For finding this probability we have to find z score.

That is we have to find P(Z > 1)

P(Z > 1) = 1 - P(Z < 1) = 1 - 0.8413 = 0.1587 ( Using z table)

b)

P(X < 212.23)

For finding this probability we have to find z score.

That is we have to find P(Z < 2)

P(Z < 2) = 0.9772 ( Using z table)

c)

P( 183.55 < X < 212.23)

For finding this probability we have to find z score.

That is we have to find P( - 2 < Z < 2)

P( - 2 < Z < 2) = P(Z < 2) - P(Z < - 2 ) = 0.9772 - 0.0228 = 0.9545

( From z table)

d) P(Z > 210)

For finding this probability we have to find z score.

That is we have to find P(Z > 1.69)

P(Z > 1.69) = 1 - P(Z < 1.69) = 1 - 0.9544 = 0.0456

It is below 0.05 so it is unusual.

P(X < 180)

For finding this probability we have to find z score.

That is we have to find P(Z < - 2.50)

P(Z < - 2.50) = 0.0063

It is below 0.05 so it is unusual.