scores on a history test have average of 80 with standard deviation of 5. What is the probability that someone will score receive a score less than 72?

Answer 1

x = score N(80,5) (normal with mean 80 standard deviation 5)

z = (x - 80)/5 is N(0,1) (normal with mean 0 and standard deviation 1 - standard normal distribution)

P(x < 72) = P(z < (72-80)/5) = P(z < -1.6) = 0.0548 (from standard normal probability table)