Normal Random Variable Probability

[needhelp83]

If X is a normal rv with mean 80 and standard deviation 10, compute the following probabilities by standardizing:

P(|X-80| <= 10)

I know how to determine the probability without absolute value, but this confuses me. Any help?

 

[Fightfish]

From |X-80| <= 10, you can get -10 <= (X-80) <= 10, -1 <= Z <= 1
We also know that P(Z<-1) = P(Z>1) due to symmetry. Hope that helps.

 

[needhelp83]

From |X-80| <= 10, you can get -10 <= (X-80) <= 10, -1 <= Z <= 1
We also know that P(Z<-1) = P(Z>1) due to symmetry. Hope that helps.

I do understand partially. I remember this from just basic algebra. Afterwards, would I solve for P(70 <= X <= 90) where I added 80 to both sides?

 

[Fightfish]

I do understand partially. I remember this from just basic algebra. Afterwards, would I solve for P(70 <= X <= 90) where I added 80 to both sides?

Yup.

 

[needhelp83]

Ok I am not getting this to work out correctly:

P(|X-80|) \leq 10)

P(-10 \leq X-80 \leq 10)

P( \frac{-10-80}{10} \leq Z \leq \frac{10-80}{10})

-9 \leq Z \leq -7

Ok, so these aren't on the Z table, so I am definitely not doing something right. What am I now missing? The 80 is my mean and 10 is my s.d.

 

[Fightfish]

Z = \frac{X-\mu}{\sigma}
Check your standardisation.

 

[needhelp83]

P(-10 \leq X-80 \leq 10)

P (70 \leq X \leq 90)

P (\frac{70-80}{10} \leq Z \leq \frac{90-80}{10})

.1587-.8413 = -0.6826

I am funny! What a silly mistake. Should be right now!

 

[statdad]

Check your final calculation - you have a glaring error.

 

[needhelp83]

Check your final calculation - you have a glaring error.

Wow, this problem kicked my butt!

ANSWER IS:
0.8413 - 0.1587 =0.6826

Thanks for the help guys!