Suppose a certain population of observations is normally dis

Suppose a certain population of observations is normally distributed. What percentage of the observations in the population

Are within ±1.5 standard deviations of the mean?

Are more than 2.5 standard deviations above the mean?

Are more than 3.5 standard deviations away from (above or below) the mean?

Suppose a certain population of observations is normally distributed. What percentage of the observations in the population

Are within ±1.5 standard deviations of the mean?

From standard normal table,

P( -1.5<z<1.5)= P( z <1.5)- p( z < -1.5)

=0.9332-0.0668 =0.8664

The required percentage = 86.64%

Are more than 2.5 standard deviations above the mean?

P( z >2.5)=0.0062

The required percentage = 0.62%

Are more than 3.5 standard deviations away from (above or below) the mean?

P( z < -3.5) + p( z > 3.5)

= 0.0002+0.0002=0.0004

The required percentage = 0.04%