Need Help with Empirical Rule! Please! Clueless!

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peggyskold

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Need help with Empirical Rule. I just can't seem to wrap my head around this? Have been trying to do this problem since yesterday. If anyone can tell me how to solve it I would so very much appreciate it.

Human pregnancy lengths are bell-shaped with a mean of 265 days and a standard deviation of 10 days. Use the Empirical Rule to determine the percent of women whose pregancies are between 255 and 275 days.

I have been trying to understand this by studying the bell-shaped distribution but I just cannot figure out what formula to plug these numbers in to get the answer--so that it makes sense to me? By looking at the bell shaped distibution and the part of the rule that says 68% of the data lie within one standard deviation of the mean--I want to say that 255 would be one deviation to the left and and 275 would be one deviation to the right, so would that be 68%? I don't think so???

Help anyone!!!
 
Re: Probability/Statistics

peggyskold said:
Need help with Empirical Rule. I just can't seem to wrap my head around this? Have been trying to do this problem since yesterday. If anyone can tell me how to solve it I would so very much appreciate it.

Human pregnancy lengths are bell-shaped with a mean of 265 days and a standard deviation of 10 days. Use the Empirical Rule to determine the percent of women whose pregancies are between 255 and 275 days.

I have been trying to understand this by studying the bell-shaped distribution but I just cannot figure out what formula to plug these numbers in to get the answer--so that it makes sense to me?

Help anyone!!!
Click to expand...

What emperical rules have you been taught about this topic?

Have studied z-distribution?
 
Re: Probability/Statistics

I guess it is the "68-95-99.7" rule.
1)About 68% of the data lie within one standard deviation of the mean.
2)About 95% of the data lie within two standard deviations of the mean.
3)About 99.7% of the data lie within three standard deviations of the mean.

Lost?
 
Re: Probability/Statistics

peggyskold said:
I guess it is the "68-95-99.7" rule.
1)About 68% of the data lie within one standard deviation of the mean. <<< This is the situation you have
2)About 95% of the data lie within two standard deviations of the mean.
3)About 99.7% of the data lie within three standard deviations of the mean.

Lost?
Click to expand...

265 ± 10 = 255 - 275
 
peggyskold said:
Need help with Empirical Rule. I just can't seem to wrap my head around this? Have been trying to do this problem since yesterday. If anyone can tell me how to solve it I would so very much appreciate it.

Human pregnancy lengths are bell-shaped with a mean of 265 days and a standard deviation of 10 days. Use the Empirical Rule to determine the percent of women whose pregancies are between 255 and 275 days.

I have been trying to understand this by studying the bell-shaped distribution but I just cannot figure out what formula to plug these numbers in to get the answer--so that it makes sense to me? By looking at the bell shaped distibution and the part of the rule that says 68% of the data lie within one standard deviation of the mean--I want to say that 255 would be one deviation to the left and and 275 would be one deviation to the right, so would that be 68%? I don't think so??? Why - what makes you think that would be incorrect?
Help anyone!!!
Click to expand...
 
Just looking at the bell curve, we can see that since the SD is 10, then 255 is 1 SD below the mean. Since 68% falls within 1 SD of the mean, then that is 34% below.

The 275 is 1 above. See?. 275-265=10. 10 is one SD.

255-265=-1. 1 SD below.

The z value comes from negative infinity. Since we are 1 above and 1 below, the percentage is about 68% just by looking at the graph and without calculating anything.

But, to do it the more exact way:

\(\displaystyle z=\frac{x-{\mu}}{\sigma}\)

\(\displaystyle \frac{265-255}{10}=1\)

Look up 1 in the table and we see the corresponding value is .8413.

.8413-.5=.3413

We subtract .5 because it is in the center and is half the area of the graph.

Do the same for 275 and we get -1

The corresponding value is .1587

.5-.1587=.3413

Add them and get .6826 or 68.26%

Which is close enough to what the Empirical Rule states.

You can easily see from the graph that 1 above is 34% and 1 below is 34%. Together they're 68%.

Always look at the SD and the mean. In this case, the x values are nice and even in that they are each 1 SD from the mean

275-265=10 and 265-255=10.
 

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Thanks so very, very much! So I was right after all--but I think I will be able to understand this a little better. Thanks again
Peggy
 
peggyskold said:
O.k. I get that but how do I caluculate the percentage?
Click to expand...

Cody (Galactus) showed you the explanation behind the "emperical" rule.

As an emperical rule however, you just need to remember it - not calculate it (which is quite cumbersome - requiring tables and all that).
 
Hello,

Could someone tell me what table is used when determining the percentage of observations with Emperical rule?
 
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