# normal distribution -help!

• Feb 3rd 2009, 04:46 AM
okello
normal distribution -help!
In a normal distribution 31% of the items are under 45 and 8% are over 64. Find the mean and S.D. of the distribution.

I need some help on the above number. Thanx.
• Feb 3rd 2009, 04:56 AM
mr fantastic
Quote:

Originally Posted by okello
In a normal distribution 31% of the items are under 45 and 8% are over 64. Find the mean and S.D. of the distribution.

I need some help on the above number. Thanx.

$\Pr(X < 45) = 0.31$.

Find the value $a$ of $Z$ such that $\Pr(Z < a) = 0.31$.

From $Z = \frac{X - \mu}{\sigma}$ it follows that $a = \frac{45 - \mu}{\sigma}$.

Substitute your value of $a$ to get equation (1) with the unknowns $\mu$ and $\sigma$.

$\Pr(X > 64) = 0.08$.

Find the value $b$ of $Z$ such that $\Pr(Z > b) = 0.08$.

From $Z = \frac{X - \mu}{\sigma}$ it follows that $b = \frac{64 - \mu}{\sigma}$.

Substitute your value of $b$ to get equation (2) with the unknowns $\mu$ and $\sigma$.

Solve equations (1) and (2) simultaneously.
• Feb 3rd 2009, 09:20 AM
okello
normal distribution - help!
Hi Mr. Fantastic, thanx.

I got http://www.mathhelpforum.com/math-he...3c147d21-1.gif as -82.6 and http://www.mathhelpforum.com/math-he...88de1d0a-1.gif as 70.6 using a calculator.

Kindly confirm. Thanks once again.

Regards,
Okello
• Feb 3rd 2009, 11:42 AM
mr fantastic
Quote:

Originally Posted by okello
Hi Mr. Fantastic, thanx.

I got http://www.mathhelpforum.com/math-he...3c147d21-1.gif as -82.6 and http://www.mathhelpforum.com/math-he...88de1d0a-1.gif as 70.6 using a calculator.

Kindly confirm. Thanks once again.

Regards,
Okello

I doubt $\sigma$ is correct - for starters you have it negative!! Even ignoring the -ve as a typo it's size is way too big.

If you post your calculations I will review them for the mistake(s) (but be patient because I'm very busy and might take some time to post).
• Feb 6th 2009, 04:00 AM
okello
normal distribution - help!
• Feb 6th 2009, 04:11 AM
mr fantastic
Quote:

Originally Posted by okello

Quote:

Originally Posted by mr fantastic
$\Pr(X < 45) = 0.31$.

Find the value $a$ of $Z$ such that $\Pr(Z < a) = 0.31$.

Mr F adds: This does NOT mean that a = 0.31.

[snip]

$\Pr(X > 64) = 0.08$.

Find the value $b$ of $Z$ such that $\Pr(Z > b) = 0.08$.

Mr F adds: This does NOT mean that b = 008.

[snip]

If $\Pr(Z < a) = 0.31$ then you're expected to be able to get (using tables or technology) that a = -0.4959 since $\Pr(Z < -0.4959) = 0.31$

Similar with b.

This is the inverse normal problem - you must have met questions like this in your earlier work ....
• Feb 15th 2009, 07:10 PM
matheagle
Quote:

Originally Posted by okello
Hi Mr. Fantastic, thanx.

I got http://www.mathhelpforum.com/math-he...3c147d21-1.gif as -82.6 and http://www.mathhelpforum.com/math-he...88de1d0a-1.gif as 70.6 using a calculator.

Kindly confirm. Thanks once again.

Regards,
Okello

A negative standard deviation?
This is why I don't like seeing calculators in my class, especially integral calculators.
• Feb 16th 2009, 02:19 AM
okello
normal distribution - help!
Hi Matheagle,
Have you calculated it?. What answer did you get?

Regards,
• Feb 16th 2009, 02:28 AM
mr fantastic
Quote:

Originally Posted by okello
Hi Matheagle,
Have you calculated it?. What answer did you get?

Regards,

Wrong questions.

Here are the correct questions:

Hi okello,
Have you calculated b? What answer did you get?
• Feb 16th 2009, 05:27 PM
matheagle
I'm going to put a similar problem on my exam next week.