Question

For 300 trading​ days, the daily closing price of a stock​ (in $) is well modeled by a Normal model with mean

​$196.12

and standard deviation

​$7.12

According to this​model, what cutoff value of price would separate the

​a) lowest

11​%

of the​ days?

​b) highest

0.77%?

​c) middle

52%?

​d) highest

50%?

Answer 1

Solution:-

Mean = 196.12, S.D = 7.12

a) The cutoff value of price would separate the lowest 11​% of the​ days is 187.264.

p-value for the lowest 11% = 0.11

z-score for the p-value = -1.227

By applying normal distribution:-

$z = \frac{x-\mu }{\sigma }$

x = 187.264

​b) The cutoff value of price would separate the highest 0.77% is 206.273.

p-value for the highest 0.77% = 1 - 0.077 = 0.923

z-score for the p-value = 1.426

By applying normal distribution:-

$z = \frac{x-\mu }{\sigma }$

x = 206.273

​c) The cutoff value of price would separate the middle 52% is 191.09 and 201.15.

p-value for the middle 52% = 0.24 and 0.76

z-score for the p-value = + 0.706

By applying normal distribution:-

$z = \frac{x-\mu }{\sigma }$

x₁ = 191.093

x₂ = 201.147

​d) The cutoff value of price would separate the highest 50% is 196.12.

p-value for the top 50% = 0.50

z-score for the p-value = 0.00

By applying normal distribution:-

$z = \frac{x-\mu }{\sigma }$

x = 196.12