Question

Find the proportion of heights that are within 1 standard deviation of the sample mean and also the proportion that are within 2 standard deviations of the sample mean. use the unrounded values for the mean and standard deviation when doing this calculation. give your answers as decimals to 2 decimal places.

Answer 1

For a normal distribution only, for a population, not for particular sample.

proportion between 1 standard deviation, independent of μ and σ , is given by:
P(Z<1)-P(Z<-1)
=0.841345-0.158655=0.682689
=0.68  (to two places of decimal)

proportion between 2 standard deviations, independent of &mu; and &sigma; , is given by:
P(Z<2)-P(Z<-2)
=0.977250-0.022750=0.954500=0.95  (to two places of decimal)