Test scores on a lab test are normally distributed with mean of 200. If standard deviation is 20, what % fall between 180 & 240

Answer 1

x = score N(200,20)

z = (x - mean)/SD = (x - 200)/20 is distributed N(0,1)

z scores and associated probabilities contained in standard normal probabilities table.

P(180 < x < 240) = P( (180-200)/20 < z < (240-200)/20) = P(-1 < z < 2) = P(z < 2) - P(z < -1) = 0.9772 - 0.1587 = 0.8185