Question

For 300 trading​ days, the daily closing price of a stock​ (in $) is well modeled by a Normal model with mean ​$197.54 and standard deviation ​$7.14 . According to this​ model, what cutoff value of price would separate the ​a) lowest 17 ​% of the​ days? ​b) highest 0.07 ​%? ​c) middle 57 ​%? ​d) highest 50 ​%?

Answer 1

Solution :

mean = = 197.54

standard deviation = = 7.14

(a)

P(Z < z) = 0.17

P(Z < -0.9542) = 0.17

z = -0.9542

Using z-score formula,

x = z * +

x = -0.9542 * 7.14 + 197.54 = 190.73

Cutoff value = 190.73

(b)

P(Z > z) = 0.07%

1 - P(Z < z) = 0.0007

P(Z < z) = 1 - 0.0007

P(Z < 3.195) = 0.9993

z = 3.195

Using z-score formula,

x = z * +

x = 3.195 * 7.14 + 197.54 = 220.35

Cutoff value = 220.35

(c)

Middle 57% has the z values : -0.7892 , +0.7892

x = -0.7892 * 7.14 + 197.54 = 191.91

x = 0.7892 * 7.14 + 197.54 = 203.17

Cut off values are : 191.91 and 203.17

(d)

Highest 50% has the z value 0

Cutoff value = mean = 197.54