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 $.35 and a standard deviation of $.33. Based on this information, what is the probability that a randomly selected stock will close up $.75 or more?
A) 0.3869
B) 0.1131
C) 0.7100
D) 0.8869

Question

Quizplus · Accepted Answer

To find the probability that a randomly selected stock will close up $.75 or more, we use the Z-score formula: Z = (X - μ) / σ, where X is the value of interest ($.75), μ is the mean ($.35), and σ is the standard deviation ($.33). Plugging in the values, we get Z = ($.75 - $.35) / $.33 ≈ 1.21. Looking up the Z-score of 1.21 in a standard normal distribution table or using a calculator, we find that the area to the left of Z is approximately 0.8869. Since we're interested in the probability of closing up $.75 or more (the right tail), we subtract this value from 1 to get the probability of the right tail, which is 1 - 0.8869 = 0.1131.

Assuming That the Change in Daily Closing Prices for Stocks