Question

in a normal distribution, what percent of the bales lie: below the mean, above the mean, within one standard deviation of the mean, within two standard deviation of the mean within three standard deviations of the mean?

Answer 1

i) P(Z < 0) = 0.50 = 50%

In a normal distribution 50% of the bales lie below the mean.

ii) P(Z > 0)

   = 1 - P(Z < 0)

   = 1 - 0.5

   = 0.5 = 50%

50% of the bales lie above the mean.

iii) P(-1 < Z < 1)

= P(Z < 1) - P(Z < -1)

= 0.8413 - 0.1587

= 0.6826 = 68.26%

68.26% of the bales lie within one standard deviation from the mean.

iv) P(-2 < Z < 2)

= P(Z < 2) - P(Z < -2)

= 0.9772 - 0.0228

= 0.9544 = 95.44%

95.44% of the bales lie within two standard deviation from the mean.

v) P(-3 < Z < 3)

= P(Z < 3) - P(Z < -3)

= 0.9987 - 0.0013

= 0.9974 = 99.74%

99.74% of the bales lie within three standard deviation from the mean.