Question

The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $16 and $30 per share.

What is the probability that the stock price will be:_______
a) More than $25? (Round your answer to 4 decimal places.)
b) Less than or equal to $18? (Round your answer to 4 decimal places.)

Answer 1

a) 0.3571 = 35.71% probability that the stock price will be more than $25.

b) 0.1429 = 14.29% probability that the stock price will be less than or equal to $18.

Explanation:

Uniform probability distribution:

An uniform distribution has two bounds, a and b.

The probability of finding a value of at lower than x is:

`P(X < x) = (x - a)/(b - a)`

The probability of finding a value between c and d is:

`P(c \leq X \leq d) = (d - c)/(b - a)`

The probability of finding a value above x is:

`P(X > x) = (b - x)/(b - a)`

Uniformly distributed between $16 and $30 per share.

This means that
`a = 16, b = 30`

a) More than $25?

`P(X > x) = (30 - 25)/(30 - 16) = 0.3571`

0.3571 = 35.71% probability that the stock price will be more than $25.

b) Less than or equal to $18?

`P(X < 18) = (18 - 16)/(30 - 16) = 0.1429`

0.1429 = 14.29% probability that the stock price will be less than or equal to $18.