Assuming that the change in daily closing prices for stocks on the New York Stock Exchange is a random variable that is normally distributed with a mean of $0.35 and a standard deviation of $0.33. Based on this information, what is the probability that a randomly selected stock will be lower by $0.40 or more?
A) 2.27
B) 0.4884
C) 0.0116
D) 0.9884

Question

Quizplus · Accepted Answer

To find the probability that a randomly selected stock will be lower by $0.40 or more, we need to calculate the Z-score for a change of -$0.40 (since a decrease is represented by a negative value). The Z-score formula is $Z = \frac{X - \mu}{\sigma}$, where $X$ is the value of interest, $\mu$ is the mean, and $\sigma$ is the standard deviation. Plugging in the values, we get $Z = \frac{-0.40 - 0.35}{0.33} = \frac{-0.75}{0.33} \approx -2.27$. Looking up -2.27 on the standard normal distribution table gives us a left-tail probability of approximately 0.0116, which means there's about a 1.16% chance a randomly selected stock will be lower by $0.40 or more.

Assuming That the Change in Daily Closing Prices for Stocks