The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $23 and $37 per share.
What is the probability that the stock price will be:
More than $33?
Less than or equal to $27?
(37-33)/(37-23) = ?
(27-23)/(37-23) = ?
To find the probability of the stock price being more than $33, we need to calculate the area under the probability distribution curve for values greater than $33.
Since the stock price is uniformly distributed between $23 and $37, the total area under the curve is equal to 1. The probability density function for a uniform distribution is given by:
f(x) = 1 / (b - a)
where 'a' is the lower bound of the distribution ($23 in this case) and 'b' is the upper bound of the distribution ($37).
To find the probability of the stock price being more than $33, we need to find the area under the curve between $33 and $37:
P(X > $33) = ∫[33, 37] f(x) dx
P(X > $33) = (∫[33, 37] 1 / (37 - 23) dx
P(X > $33) = [x / (37 - 23)] |[33, 37]
P(X > $33) = [(37 / (37 - 23)) - (33 / (37 - 23))]
P(X > $33) = (37 / 14) - (33 / 14)
P(X > $33) = 4 / 14
P(X > $33) = 2 / 7
Therefore, the probability that the stock price will be more than $33 is 2/7, or approximately 0.2857.
To find the probability of the stock price being less than or equal to $27, we need to find the area under the curve between $23 and $27:
P(X ≤ $27) = ∫[23, 27] f(x) dx
P(X ≤ $27) = (∫[23, 27] 1 / (37 - 23) dx
P(X ≤ $27) = [x / (37 - 23)] |[23, 27]
P(X ≤ $27) = [(27 / (37 - 23)) - (23 / (37 - 23))]
P(X ≤ $27) = (27 / 14) - (23 / 14)
P(X ≤ $27) = 4 / 14
P(X ≤ $27) = 2 / 7
Therefore, the probability that the stock price will be less than or equal to $27 is 2/7, or approximately 0.2857.