Need Help with Empirical Rule! Please! Clueless!

[peggyskold]

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!!!

 

[Deleted member 4993]

Re: Probability/Statistics

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!!!

What emperical rules have you been taught about this topic?

Have studied z-distribution?

 

[peggyskold]

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?

 

[Deleted member 4993]

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. <<< 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?

265 ± 10 = 255 - 275

 

[Deleted member 4993]

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!!!

 

[peggyskold]

O.k. I get that but how do I caluculate the percentage?

 

[galactus]

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.

 

[peggyskold]

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

 

[Deleted member 4993]

O.k. I get that but how do I caluculate the percentage?

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).

 

[resp7]

Hello,

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