The closing price of Schnur Sporting Goods Inc common stock

The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $22 and $37 per share.

Solution

PDF of Uniform Distribution f(x) = 1 / ( b - a ) for a < x < b
b = Maximum Value
a = Minimum Value
Mean = a + b / 2
Standard Deviation = Sqrt ( ( b - a ) ^ 2 / 12 )

f(x) = 1/(b-a) = 1 / (37-22) = 1 / 15 = 0.0667
a)
P(X > 30) = (37-30) * f(x)
= 7*0.0667
= 0.4669
b)
P(X > 29) = (37-29) * f(x)
= 8*0.0667
= 0.5336
P( X < = 29 ) = 1 - P(X > 29) = 1 - 0.534 = 0.4664