1. ## 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.

2. 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.

3. ## normal distribution - help!

Hi Mr. Fantastic, thanx.

I got as -82.6 and as 70.6 using a calculator.

Kindly confirm. Thanks once again.

Regards,
Okello

4. Originally Posted by okello
Hi Mr. Fantastic, thanx.

I got as -82.6 and 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).

5. ## normal distribution - help!

Hi Mr. Fantastic,

and =0.08 ...................(ii)

implying that

0.31 + = 45 -----iii
0.08 + = 64 ------iv

And used calc to find 2 unknowns. And I got as -82.6 and as 70.6 using a calculator.

Thanks

6. Originally Posted by okello
Hi Mr. Fantastic,

and =0.08 ...................(ii)

implying that

0.31 + = 45 -----iii
0.08 + = 64 ------iv

And used calc to find 2 unknowns. And I got as -82.6 and as 70.6 using a calculator.

Thanks
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 ....

7. Originally Posted by okello
Hi Mr. Fantastic, thanx.

I got as -82.6 and 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.

8. ## normal distribution - help!

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

Regards,

9. 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?

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

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# In normal distribution 31% of the items are under 45 and 8% are over 64. Find the mean and variance of the distribution

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