Question

For 300 trading days, the daily closing price of a stock (in $) is well modeled by a Normal distribution with a mean of $197.31 and a standard deviation of $7.16. According to this model, what is the probability that the stock price is between $187.15 and $207.47?

Answer 1

The probability that the stock price is between $187.15 and $207.47 is approximately 80.84%.

Step-by-step explanation:

In order to find the probability that the stock price is between $187.15 and $207.47, we need to standardize these values using the formula:

Z = (X - μ) / σ

Where Z is the standard score, X is the value, μ is the mean, and σ is the standard deviation.

For the given values, Z1 = (187.15 - 197.31) / 7.16 = -1.421

And Z2 = (207.47 - 197.31) / 7.16 = 1.421

Now, we can use the standard normal distribution table or a calculator to find the area under the curve between these two Z-scores.

The area between -1.421 and 1.421 is approximately 0.8084 or 80.84%.