# If X is normally distributed w

If X is normally distributed with a mean of 30 and astandard deviation of 2, find P(30 ≤ X ≤ 33.4).

a) 0.455

b) 0.855

c) 0.955

d) 0.555

e) 0.755

f) None of the above

Solution:

Given: X is normally distributed with a mean of 30 anda standard deviation of 2

That is: X ~ Normal

We have to find:

Find z scores for x = 30 and for x= 33.4

Thus we get:

Look in z table for z = 0.0 and 0.00 as well as for z = 1.7 and0.00 and find area.

P( Z< 0.00) = 0.5000

P( Z < 1.70) =0.9554

Thus

Thus correct option is: a) 0.455

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