In: Statistics and Probability
A normal distribution has μ = 30 and σ = 5.
(a) Find the z score corresponding to
x = 25.
b) Find the z score corresponding to
x = 42.
(c) Find the raw score corresponding to
z = −2.
(d) Find the raw score corresponding to
z = 1.9.
Solution :
Given that
mean = = 30
standard deviation = = 5
a ) x = 25
Using z-score formula,
z = x - /
= (25 - 30 / 5 )
= - 5 / 5
= -1
z = -1
b ) x = 42
Using z-score formula,
z = x - /
= (42 - 30 / 5 )
= 8 / 5
= 1.6
z = 1.6
(c) The raw score corresponding to
z = −2.
Using z-score formula,
x = z * +
x = - 2 * 5 + 30
= - 10 +30
= 20
The raw score = 20
(d) The raw score corresponding to
z = 1.9
Using z-score formula,
x = z * +
x = 1.9 * 5 + 30
= 9.5 + 30
= 39.5
The raw score = 39.5