The Normal Distribution

Question

A variable x� is normally distributed with mean 15 and standard deviation 8.

Round your answers to the nearest hundredth as needed.

a) Determine the z�-score for x=19�=19.

1. z=�=

b) Determine the z�-score for x=11�=11.

1. z=�=

c) What value of x� has a z�-score of 0.750.75?

1. x=�=

d) What value of x� has a z�-score of 00?

1. x=�=

e) What value of x� has a z�-score of 00?

1. x=�=

Answer 1

z = (x - mean) / (standard deviation)

So, if x = 19, then z = (19 - 15) / 8 = 4/8 = 0.5. This means that 19 is 0.5 standard deviations above the mean.

if x = 11, then z = (11 - 15) / 8 = -4/8 = -0.5. This means that 11 is 0.5 standard deviations below the mean.

etc

Answer 2

z = (μ - X) / σ, where μ is the mean and σ is the standard deviation

Now go for it!