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In: Math

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 a mean of

$197.12197.12 and a standard deviation of

$7.187.18. 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 $204.30204.30?

b) below $211.48211.48?

c) between $182.76182.76 and $211.48211.48?

Expert Solution

Solution :

Given that ,

mean = = 197.12

standard deviation = = 7.18

(a)

P(x > 204.30) = 1 - P(x < 204.30)

= 1 - P((x - ) / < (204.30 - 197.12) / 7.18)

= 1 - P(z < 1)

= 1 - 0.8413

= 0.1587

P(x > 204.30) = 0.1587

Probability = 0.1587

(b)

P(x < 211.48) = P((x - ) / < (211.48 - 197.12) / 7.18)

= P(z < 2)

Using standard normal table,

P(x < 2) = 0.9772

Probability = 0.9772

(c)

P(182.76< x < 211.48) = P((182.76 - 197.12)/ 7.18) < (x - ) / < (211.48 - 197.12) / 7.18) )

= P(-2 < z < 2)

= P(z < 2) - P(z < -2)

= 0.9772 - 0.0228

= 0.9544

Probability = 0.9544

milcah answered 7 months ago

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