Question

Suppose that a stock is currently selling for $100. The change in the stock's price during the next year follows a normal random variable with a mean of $10 and a standard deviation of $20. What is the probability (rounded to the nearest hundredth) that the stock will sell for at least $120 in a year's time?

Answer 1

Answer:

Step-by-step explanation:

The probability of the stock to be above 120 dollars is equivalent to the probability of the random variable to be above 20 dollars. Since the random variable follow a normal distribution (with a mean of $10 and a standard deviation of $20), we can compute the probability using the following formula (Cumulative Distribution Function)

Note that this formula gives the probability of a normal random variable to be below x (below 20 in your case), mu being the mean and sigma being the standard deviation. The result is 0.69.

Since we want the probability of being above $20, we just compute 1-0.69=0.31