calculate using excel 1) suppse that the annual return on XYZ stock follows a no

ID: 3325008 • Letter: C

Question

calculate using excel

1) suppse that the annual return on XYZ stock follows a normal distribution with mean 14% and standard deviation 2.1%

a) what is the probability that XYZ's value will decrease during the following year? (i.e percent return will be less than 0%)

B) what is the probability thst XYZ's return will be greater than 15%?

C) for what percent return value does XYZ stock have only a 5% chance of exceeding that value?

D) what is the probability of XYZ's rate of return will fall between 10% and 18%?

A) P(x < 0)

= P((x - mean)/SD < (0 - mean)/SD)

= P(Z < (0 - 0.14)/0.021)

= P(Z < -6.67)

= 0

B) P(X > x) = 0.05

Or, P((X - mean)/SD > (x - 0.14)/0.021) = 0.05

Or, P(Z > (x - 0.14)/0.021) = 0.05

Or, P(Z < (x - 0.14)/0.021) = 0.95

Or, (x - 0.14)/0.021 = 1.645

Or, x = 1.645 * 0.021 + 0.14

Or, x = 0.1745 = 17.45%

C) P(x > 0.05)

= P((x - mean)/SD > (0.05 - mean)/SD)

= P(Z > (0.05 - 0.14)/0.021)

= P(Z > -4.28)

= 1 - P (Z < -4.28)

= 1 - 0 = 1 = 100%

D) P(0.1 < x < 0.18)

= P((0.1 - 0.14)/0.021 < Z < (0.18 - 0.14)/0.021)

= P(-1.9 < Z < 1.9)

= P(Z < 1.9) - P(Z < -1.9)

= 0.9713 - 0.0287 = 0.9426

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