Question

In: Statistics and Probability

A normal distribution has μ = 30 and σ = 5. (a) Find the z score...

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.

Solutions

Expert Solution

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

orchestra answered 2 years ago
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