Question

a data set mean 14 and standard deviation 2. Approximately 68% of the observations lie between ____ and _____

Answer 1

Solution :

Given that ,

mean = = 14

standard deviation = = 2

middle 68% of score is

P(-z < Z < z) = 0.68

P(Z< z) - P(Z < -z) = 0.68

2P(Z < z) - 1 = 0.68

2P(Z < z) = 1 + 0.68 = 1.68

P(Z < z) = 1.68 / 2 = 0.84

P(Z < 1) = 0.84 ( using standard normal table)

middle 68% has two z value -1 and +1

z = -1 and z=1

Using z-score formula,

x = z *middle 68% of score is

P(-z Z z) = 0.68

P(Z z) - P(Z -z) = 0.68

2P(Z z) - 1 = 0.68

2P(Z z) = 1 + 0.68 = 1.68

P(Z z) = 1.68 / 2 = 0.84

P(Z 1) = 0.84

middle 68% has two z value -1 and +1

z = -1

Using z-score formula,

x = z * +

x = -1*2+ 14

x =-12

x = z * +

x = 1*2+ 14

x =16

68% of the observations lie between ___-12_ and ___16__