Question

approximately 95 of all values of a normally distributed populations lie within how many standard deviations of the population mean

Answer 1

Solution,

Using standard normal table,

P( -z < Z < z) = 95%

= P(Z < z) - P(Z <-z ) = 0.95

= 2P(Z < z) - 1 = 0.95

= 2P(Z < z) = 1 + 0.95

= P(Z < z) = 1.95 / 2

= P(Z < z) = 0.975

= P(Z < 2.0) = 0.975

= z  ± 2.0

P( - 2 < x <   + 2 ) = 95%

2 standard deviations of the population mean