SAT scores in one state is normally distributed with a mean of 1481 and a standard deviation of 88. Suppose we randomly pick 49 SAT scores from that state. a) Find the probability that one of the scores in the sample is less than 1457. P(X<1457)P(X<1457) = b) Find the probability that the average of the scores for the sample of 49 scores is less than 1457. P(¯¯¯X<1457)P(X¯<1457) =

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.