Question

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

​$197.38 and standard deviation

​$7.16

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

​a) lowest

13%

of the​ days?

​b) highest

0.62%?

​c) middle

79​%?

​d) highest

50​%?

Select the correct answer below and fill in the answer​ box(es) within your choice.

A.The cutoff points are

nothing

and

nothing.

​(Use ascending order. Round to two decimal places as​ needed.)

B.The cutoff point is

nothing.

​(Round to two decimal places as​ needed.)

Answer 1

We are given the distribution here as:

a) From standard normal tables, we have:
P( Z < -1.126) = 0.13

Therefore, the cutoff value here is computed as:
= Mean  -1.126*Std Dev

= 197.38 -1.126*7.16

= 189.31784

Therefore 189.32 days is the required value here.

b) From standard normal tables, we have here:
P(Z < 2.501) = 0.9938,

Therefore, P(Z > 2.501) = 1 - 0.9938 = 0.0062

Therefore the cutoff value here is computed as:
= 197.38 + 2.501*7.16

= 215.29

Therefore 215.29 days is the required cutoff value here.

c) For middle 79%, we have:
P(-c < Z < c ) = 0.79

Therefore, P(Z < c) = 0.79 + (1 -0.79)/2 = 0.895

From standard normal tables, we have here:
P(Z < 1.254) = 0.895

Therefore the cut off values here are computed as:

Mean - 1.254*Std Dev , Mean + 1.254 * Std Dev

197.38 - 1.254*7.16, 197.38 + 1.254*7.16

197.38 - 8.98, 197.38 + 8.98

188.40, 206.36

These are the required values here.

d) Note that the normal distribution is symmetric about its mean, therefore:
P(X > Mean) = P(X < Mean) = 0.5

Therefore the cutoff value here is 197.38 days.