Hi I know how to calculate standard deviation but am having trouble with questions the in the image. Please help.. Either 8 or 10 worked out would be a huge help.

Printable View

- January 25th 2006, 10:17 AMArbiturStandard Deviation and Normal Distribution
Hi I know how to calculate standard deviation but am having trouble with questions the in the image. Please help.. Either 8 or 10 worked out would be a huge help.

- January 25th 2006, 12:53 PMThePerfectHacker
Since 173 is the mean and standard deviation is 7.7 cm. Thus, One standard deviation to the left and right takes 68% (a rule) thus, 165.3-180.7 take 68% of all the students. Thus 32% below 165.3 or above 180.7 cm. Now the normal distribution is symettric thus, 16% below 165.3 and 16% aboce 180.7 cm. Look at the problem it say the taller 15% thus, approximately the taller 16% thus the range is approximately 180.7 cm.

- January 25th 2006, 12:57 PMThePerfectHacker
Look at the hint to look for the lower part of normal distribution. This problem unlike the first requires you to move 2 standard deviations. This will take on 95% (a rule) thus, between .9-4.1 years are included in these 95%. Thus, 5% below .9 or above 4.1 years. But because the normal distribution is symettric thus, 2.5% below .9 years or above 4.1 years. The problem asks for the 2.5% thus the range is .9 years.

- January 25th 2006, 02:37 PMArbitur
thanks... I know what your saying but could you just show how you calculated just one of those if possible? Thanks.

- January 25th 2006, 03:06 PMThePerfectHacker
Let be the precentage (or probability) of all values between and .

There is a theorem (theorem-1) in statistics that if something is normal distributed and is the mean, and is the standard deviation then,

.

Also because (theorem-2) the normal distribution has symettrism we have that If Then, . The reason being, because excludes the first one and then diving by 2 is because of symettrism.

Now to do problem 2, the mean and the standard deviation is . By the above explanations and theorem-1 (because 2 standard deviations). Next, use theorem-2 thus, =2.5% which you where trying to find.

Thus the answer is .

Q.E.D. - January 25th 2006, 03:09 PMArbitur
Arr.. thanks for trying but I still don't get how you got to the answer. I'll try a tutor somewhere for 1 session or something. (Taking this course online.) Thanks anyways.

- January 25th 2006, 03:23 PMArbitur
Heh.. feel stupid.. cant even figure out how you did it. Thanks neways :) guess im just not smart enough

Shouldnt it be 17% instead of 16%? - January 25th 2006, 03:59 PMThePerfectHackerQuote:

Originally Posted by**Arbitur**

- January 27th 2006, 11:48 AMCaptainBlackQuote:

Originally Posted by**Arbitur**

standard deviation , then:

,

has a standard normal distribution. The height of the beams is such that

will hit their heads, call this height .

Call the corresponding score , then:

,

So of scores exceed , or of scores are less than .

Now look up the value of which gives in a table

of the cumulative normal distribution, doing this gives .

The corresponding height (which will be the height of the beams) will be

the solution of:

,

which when we plug in the value of gives:

.

Thus all students taller than cm. will be affected.

RonL