Question

The price of a stock is uniformly distributed between $30 and $40.

a. What is the probability that the stock price will be more than \$37? 2pt
b. What is the probability that the stock price will be less than $32 ? 1pt
c. Determine the expected price of the stock. 2pt

Answer 1

The probability of the stock price being more than $37 is 30%, the probability of it being less than $32 is 20%, and the expected price of the stock is $35.

Step-by-step explanation:

The price of a stock is uniformly distributed between $30 and $40. We can answer the questions as follows:

1. Probability that the stock price will be more than $37: The range of the uniform distribution is $40 - $30 = $10. The range above $37 is $40 - $37 = $3. Therefore, the probability is $3/$10 = 0.3 or 30%.
2. Probability that the stock price will be less than $32: This range is $32 - $30 = $2. Therefore, the probability is $2/$10 = 0.2 or 20%.
3. Expected price of the stock: For a uniform distribution, the expected value is the average of the minimum and maximum values, so (30+40)/2 = $35.