The student SAT score is a random variable that follows a no

The student SAT score is a random variable that follows a normal distribution. Letting X denote this variable, the mean of X is given by 1350 and the standard deviation of X is given by 100.

(a) Draw the probability density curve of X . What is the value of X at the center of the curve? How would the density curve look like if the standard deviation were 150?

(b) X has been transformed to the following standardized normal random variable: Z = X-1350/100 . What is the mean and the standard deviation of Z ? Draw the probability density curve of Z .

(c) Compute the probability that X takes a value that is greater than 1400.

(d) Compute the probability that X takes a value that is between 1200 and 1300.

Solution