Question

For 300 trading​ days, the daily closing price of a stock​ (in $) is well modeled by a Normal model with a mean of ​$195.54 and a standard deviation of ​$7.14. 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 ​$209.82

​b) below ​$202.68​? ​

c) between ​$181.26 and ​$209.82?

Answer 1

P(X < A) = P(Z < (A - mean)/standard deviation)

Mean = $195.54

Standard deviation = $7.14

a) P(above $209.82) = P(X > 209.82)

= 1 - P(X < 209.82)

= 1 - P(Z < (209.82 - 195.54)/7.14)

= 1 - P(Z < 2)

= 1 - 0.9772

= 0.0228

b) P(below 202.68) = P(X < 202.68)

= P(Z < (202.68 - 195.54)/7.14)

= P(Z < 1)

= 0.8413

c) P(between $181.26 and 209.82) = P(X < 209.82) - P(X < 181.26)

= 0.9772 - P(Z < (181.26 - 195.54)/7.14)

= 0.9772 - P(Z < -2)

= 0.9772 - 0.0228

= 0.9544