z-scores are distributed according to the standard normal distribution. That is, with the parameters: mean 0 and variance 1.
Variance
99.7% of scores fall within -3 and plus 3 standard deviations around the mean in a normal distribution.
Scores on the SAT form a normal distribution with a mean of µ = 500 with σ = 100. What is the probability that a randomly selected college applicant will have a score greater than 640?
They are said to be Normally distributed.
The distribution is skewed to the right.
z-scores are distributed according to the standard normal distribution. That is, with the parameters: mean 0 and variance 1.
Variance
Standard deviation
Variance
99.7% of scores fall within -3 and plus 3 standard deviations around the mean in a normal distribution.
The answer depends on the degrees of freedom (df). If the df > 1 then the mean is 0, and the standard deviation, for df > 2, is sqrt[df/(df - 2)].
Scores on the SAT form a normal distribution with a mean of µ = 500 with σ = 100. What is the probability that a randomly selected college applicant will have a score greater than 640?
skewed.
The pattern is called a normal distribution, or a bell curve. It is characterized by symmetrical data points around the mean, with most scores clustering around the average and progressively fewer scores as you move away from the mean in either direction.
You can't do this without knowing the distribution of scores.
If there are n scores and one score is changed by x then the mean changes by x/n.