Question

In: Statistics and Probability

A normal distribution has μ = 32 and σ = 5. (a) Find the z score...

A normal distribution has μ = 32 and σ = 5.

(a) Find the z score corresponding to x = 27.

(b) Find the z score corresponding to x = 45.

(c) Find the raw score corresponding to z = −3.

(d) Find the raw score corresponding to z = 1.3.

Expert Solution

Solution :

Given that,

mean = = 32

standard deviation = = 5

(a)

x = 27

z = x - / = 27 - 32 / 5 = -1

z score = -1

(b)

x = 45

z = x - / = 45 - 32 / 5 = 2.6

z score = 2.6

(c)

z = -3

Using z-score formula,

x = z * +

x = -3 * 5 + 32 = 17

raw score = 17

(d)

z = 1.3

Using z-score formula,

x = z * +

x = 1.3 * 5 + 32 = 38.5

raw score = 38.5

orchestra answered 3 years ago

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