Question

Suppose X is normally distributed with ?=13 and ?= 2. Between what x-values does the middle 68.27% of the data lie? Round your answers to 1 decimal place.

For a ≤ X ≤ b,

a = ?

b = ?

Answer 1

Solution:-

Given that,

mean = = 13

standard deviation = = 2

Using standard normal table,

P( -z < Z < z) = 68.27%

= P(Z < z) - P(Z <-z ) = 0.6827

= 2P(Z < z) - 1 = 0.6827

= 2P(Z < z) = 1 + 0.6827

= P(Z < z) = 1.6827 / 2

= P(Z < z) = 0.8413

= P(Z < 1) = 0.8413

= z  ± 1

Using z-score formula,

x = z * +

x = - 1 * 2 + 13

x = 11.0

Using z-score formula,

x = z * +

x = 1* 2 + 13

x = 15.0

The middle 68.27% are from  a 11.0 ≤ X ≤ 15.0 b,  

a =11.0

b = 15.0