3301 Statistics

Question

After collecting the data, Raymond finds that the standardized test scores of the students in a school is normally distributed with mean 79 points and standard deviation 3 points. What is the probability that a randomly selected student score is less than 85 points?

Answer 1

let x = randomly selected score (normally distributed)

want to compute P(x < 85) - probability score less than 85

standardizing the score (subtract mean off 79 and divide by standard deviation of 3) to get z-statistic:

P( z < (85 - 79)/3) = P(z < 2) = 0.9772 (from standard normal probability table)