Question

For 300 trading​ days, the daily closing price of a stock​ (in $) is well modeled by a Normal model with mean ​$196.99 and standard deviation $7.12. 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 211.23​?

​b) below $204.11​?

​c) between 182.75 and $211.23​?

​d) Which would be more​ unusual, a day on which the stock price closed above ​$208 or below $185?

​a).......%

​(Round to one decimal place as​ needed.)

​b)........%

​(Round to one decimal place as​ needed.)

​c).......%

​(Round to one decimal place as​ needed.)

​d) Choose the correct answer below.

A. The more unusual day is if the stock closed above $ 208 because it has the largest absolute​ z-score.

B. The more unusual day is if the stock closed above $208 because it has the smallest​ z-score.

C. The more unusual day is if the stock closed below $185 because it has the smallest​ z-score.

D. The more unusual day is if the stock closed below $185 because it has the largest absolute​ z-score.

Answer 1

Answer:

a) 2.5% b) 84% c) 95% d) D. The more unusual day is if the stock closed below $185 because it has the largest absolute z-score.

Step-by-step explanation:

For a) b) and c) we will use the empirical rule, so, we can observe the image shown below

a) 211.23 is exactly two standard deviation above the mean, so, the probability that on a randomly selected day in this period the stock price closed above 211.23 is 2.35% + 0.15% = 2.5%  

b) 204.11 represents exactly one standard deviation above the mean, so, the probability of being below 204.11 is 50% + 34% = 84%

c) The probability of getting a value between 182.75 and 211.23 is 95%, this because 182.75 is exactly two standard deviations below the mean and 211.23 is exactly two standard deviations above the mean.

d) The z-score related to 208 is $z_{1}$ = (208-196.99)/7.12 = 1.5 and the z-score related to 185 is  $z_{2}$ = (185-196.99)/7.12 = -1.7, therefore, the more unusual day is if the stock closed below $185 because it has the largest absolute z-score.