Question

For a normal distribution, find the percentage of data that are (a) Within 1 standard deviation of the mean __________ % (b) Between ?−3.5? μ − 3.5 σ and ?+2.5? μ + 2.5 σ ____________% (c) More than 2 standard deviations away from the mean _________%

Answer 1

From Normal distribution tables

(a) Within 1 standard deviation of the mean is 68.27%

P(Mean - SD < X < Mean +SD) = P(-1 < Z < +1) = 0.6827 = 68.27%

(b) Between ?−3.5? and ?+2.5? is 99.34%

P(Mean - 3.5 SD < X < Mean + 2.5 SD) = P(-3.5 < Z < 2.5) = P(Z < 2.5) - P(Z < -3.5) = 0.99379 - 0.00023 = 0.99356 = 99.34%

(c) More than 2 standard deviations away from the mean is 4.55%

1 - P(Mean - 2*SD < X < Mean + 2*SD) = 1 - P(-2 < Z < 2) = 1 - 0.9545 = 0.0455 = 4.55%