Question

Suppose that the annual rate of return for a common biotechnology stock is normally distributed with a mean of 5% and a standard deviation of 6%. Find the probability that the one-year return of this stock will be negative. Round to four decimal places.

Answer 1

To find the probability of a negative one-year return for the biotechnology stock, calculate the area under the normal distribution curve to the left of 0 (negative return) using the z-score formula and standard normal distribution table or calculator.

Step-by-step explanation:

To find the probability that the one-year return of the biotechnology stock will be negative, we need to calculate the area under the normal distribution curve to the left of 0 (which represents the negative return).

Using the z-score formula: z = (x - μ) / σ, where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.

Substituting the given values: z = (0 - 0.05) / 0.06 = -0.8333.

Using a standard normal distribution table or calculator, we can find that the probability of a z-score less than -0.8333 is approximately 0.2023.

Answer 2

Answer: 0.2023

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Work Shown:

Compute the z score for x = 0.

z = (x - mu)/sigma

z = (0 - 0.05)/(0.06)

z = -0.83333 approximately

Then use a calculator to find that P(Z < -0.83333) = 0.2023

There's about a 20.23% chance of getting negative returns, i.e. the person will lose money on the investment.