Question

Let X ~ N(181; 19)

Find: (|X-181|> 44)

Answer 1

Let us start with expanding the probability

MEAN= 181 AND VARIANCE= 19 , Standard deviation=4.36

Since μ=181 and σ=4.36 we have:

So P ( 137<X<225 )=P ( 137−181< X−μ<225−181 )=P ((137−181)/4.36<(X−μ)/σ<(225−181)/4.36)

Since Z=(x−μ)/σ , (137−181)/4.36=−10.09 and (225−181)/4.36=10.09 we have:

P ( 137<X<225 )=P ( −10.09<Z<10.09 )

Use the standard normal table to conclude that:

P ( −10.09<Z<10.09 )=1