Suppose the daily change in price of a stock is normally distributed with mean = .20 and standard deviation = .30. What price ch

The value that distinguishes the lowest 25% of data from the highest 75% is -0.00235. Previous concepts: Normal distribution, which describes a "probability distribution that is balanced around the mean, indicating that data close to the mean occur more frequently than those further away from it". The Z-score is "a statistical measurement relating a value to the mean of a set of values, in terms of its distance in standard deviations from the mean". To solve the problem, let X represent the variable of interest in a population; we know the distribution for X is given by:... We want to find a value a to satisfy the condition:... Both conditions here are equivalent. We can apply the Z-score again to find the value a. The figure shows that the z value meeting the condition with 0.25 of the area to the left and 0.75 to the right is z = -0.674. Therefore, P(Z < -0.674) = 0.25 and P(z > -0.674) = 0.75. We can use condition (b) previously to derive... We know the z value that satisfies the equation, so we can proceed to solve for a, which gives us... Thus, the value that separates the lower 25% of data from the upper 75% is -0.00235.