z Score: When Reese Witherspoon won an Oscar as Best Actress for the movie Walk the Line, her age was converted to a z score of -0.61 when included among the ages of all other Oscar-winning Best Actresses at the time of this writing. Was her age above the mean or below the mean? How many standard deviations away from the mean is her age?
To determine whether Reese Witherspoon's age is above or below the mean, we need to understand what a z-score represents.
A z-score, also known as a standard score, measures how many standard deviations a particular value is away from the mean. A negative z-score indicates that the value is below the mean, while a positive z-score indicates it is above the mean.
In this case, Reese Witherspoon's z-score is -0.61. Since it is negative, we can infer that her age is below the mean age of all the other Oscar-winning Best Actresses.
To calculate the number of standard deviations away from the mean her age is, we can use the formula:
z = (x - mean) / standard deviation
Given that her z-score is -0.61 and we are interested in the number of standard deviations away from the mean her age is, we can rearrange the formula:
-0.61 = (x - mean) / standard deviation
Since the z-score is -0.61, we can conclude:
-0.61 * standard deviation = x - mean
To isolate the variable x (her age), we can add mean to both sides of the equation:
-0.61 * standard deviation + mean = x
Now, we can calculate her age in terms of the mean and standard deviation. However, without knowing the specific values of the mean and standard deviation for the ages of all other Oscar-winning Best Actresses, we can't provide an exact numerical answer.