normal distribution -help!

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February 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.
February 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.
February 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
February 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).
February 6th 2009, 04:00 AM
okello

normal distribution - help!

Hi Mr. Fantastic,
I made http://www.mathhelpforum.com/math-he...48f3713a-1.gif = 0.31 ..............(i)

and http://www.mathhelpforum.com/math-he...dacbc5e0-1.gif =0.08 ...................(ii)

implying that

0.31 http://www.mathhelpforum.com/math-he...3c147d21-1.gif + http://www.mathhelpforum.com/math-he...88de1d0a-1.gif = 45 -----iii
0.08 http://www.mathhelpforum.com/math-he...3c147d21-1.gif + http://www.mathhelpforum.com/math-he...88de1d0a-1.gif = 64 ------iv

And used calc to find 2 unknowns. And 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.

Await for your response.
Thanks
February 6th 2009, 04:11 AM
mr fantastic

Quote:

Originally Posted by okello

Hi Mr. Fantastic,
I made http://www.mathhelpforum.com/math-he...48f3713a-1.gif = 0.31 ..............(i)

and http://www.mathhelpforum.com/math-he...dacbc5e0-1.gif =0.08 ...................(ii)

implying that

0.31 http://www.mathhelpforum.com/math-he...3c147d21-1.gif + http://www.mathhelpforum.com/math-he...88de1d0a-1.gif = 45 -----iii
0.08 http://www.mathhelpforum.com/math-he...3c147d21-1.gif + http://www.mathhelpforum.com/math-he...88de1d0a-1.gif = 64 ------iv

And used calc to find 2 unknowns. And 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.

Await for your response.
Thanks

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 ....
February 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.
February 16th 2009, 02:19 AM
okello

normal distribution - help!

Hi Matheagle,
Have you calculated it?. What answer did you get?

Regards,
February 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?
February 16th 2009, 05:27 PM
matheagle

I'm going to put a similar problem on my exam next week.