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For 300 trading days, the daily closing price of a stock (in $) is well modeled...

For 300 trading days, the daily closing price of a stock (in $) is well modeled by a Normal model with mean $196.38 and standard deviation $7.13.

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 $203.51?

b) below $210.64?

c) between $182.12 and $210.64?

d) Which would be more unusual, a day on which the stock price closed above $206 or below $180?

Expert Solution

Solution:-

a) The probability that on a randomly selected day in this period the stock price closed is above 203.51 is 0.1587.

x = 203.51

By applying normal distribution:-

z = 1.0

P(z > 1.0) = 0.1587

b) The probability that on a randomly selected day in this period the stock price closed is below 210.64 is 0.977.

x = 210.64

By applying normal distribution:-

z = 2.0

P(z < 2.0) = 0.977

c) The probability that on a randomly selected day in this period the stock price closed is between $182.12 and $210.64 0.954 .

x₁ = 182.12

x₂ = 210.64

By applying normal distribution:-

z₁ = - 2.0

z₂ = 2.0

P( -2.0 < z < 2.0) = P(z > -2.0) - P(z > 2.0)

P( -2.0 < z < 2.0) = 0.977 - 0.023

P( -2.0 < z < 2.0) = 0.954

d) The day on which the stock price closed below $180 is more unusual.

x = 206

By applying normal distribution:-

z = 1.35

P(z > 1.35) = 0.089

x = 180

By applying normal distribution:-

z = -2.29

P(z < -2.29) = 0.011

milcah answered 1 year ago

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