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

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

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=(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((X-mu)/(\sigma)<(84.5-110)/(20))`

`=P(Z<-1.28)\\=1-P(Z<1.28)\\=1-0.89973\\=0.10027\\\approx0.10`

*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.