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 $85 or less in a year's time?

Answer 1

Answer:

The probability that the stock will sell for $85 or less in a year's time is 0.10.

Step-by-step explanation:

Let X = stock's price during the next year.

The random variable X follows a normal distribution with mean, μ = $100 + $10 = $110 and standard deviation, σ = $20.

To compute the probability of a normally distributed random variable we first need to compute the z-score for the given value of the random variable.

The formula to compute the z-score is:

$z=\frac{X-\mu}{\sigma}$

Compute the probability that the stock will sell for $85 or less in a year's time as follows:

Apply continuity correction:

P (X ≤ 85) = P (X < 85 - 0.50)

                = P (X < 84.50)

                $=P(\frac{X-mu}{\sigma}$

                $=P(Z$

*Use a z-table for the probability.

Thus, the probability that the stock will sell for $85 or less in a year's time is 0.10.