Which Options Show Normal Distribution in These Cases?

[leena19]

Homework Statement

Which of the following is/are likely to show normal distribution?
A) Numbers of cervical vertebrae in different species of mammals
B) Age distribution of children in school
C) Number of fruits in mango trees in an orchard
D) Fasting blood glucose levels of healthy people
E) Diameters of pencils manufactured in a factory

Homework Equations

The Attempt at a Solution

A normal distribution graph is bell-shaped,so A) can't be true ,cause all mammals have the same number of cervical vertebrae and I guess E)would also not show a normal distribution cause the pencils manufactured would mostly be of the same diameter.
I'm having trouble deciding between B),C) and D).

would really appreciate a quick response.
Thank you.

 

[Mapes]

Sure the pencil diameters won't be exactly the same; measured carefully, the values will differ but will cluster around an average with some distribution, presumably the normal distribution.

Will the childrens' ages cluster around a single point, with the frequency trailing off for ages on either side?

 

[leena19]

Thank you very much for replying!

Will the childrens' ages cluster around a single point, with the frequency trailing off for ages on either side?

No.

So far E) would show normal distribution.
And I'm guessing D) would also show normal distribution cause the fasting blood glucose level would be in the range of 80-120mg/100ml,so the frequency may cluster around a point and trail off on either side (of 80 and 120,maybe?)

Still having trouble with C) Number of fruits in mango trees in an orchard.
If the statement were number of trees in an orchard,I guess it won't be a normal distribution,but the number of fruits on the trees?

 

[Mapes]

One problem is that this is a vague question. I don't believe any physical value can belong to a truly normal distribution, as such a distribution allows for the possibility of arbitrary large positive and negative numbers. We can only say that the real-life distribution is approximately normal. So while a pencil diameter cannot be negative, the variance of actual pencil diameters is so small that if we fit a normal distribution to a sample, the predicted frequency of negative-diameter pencils would be effectively zero (say, 10^-50, for example). But what if part of the manufacturing process is discarding pencils that lie more than one standard deviation away from the mean? Obviously this would produce a non-normal (specifically, a truncated normal) distribution. So we have to make some assumptions and try to guess what the question-writer was looking for.

Here's another question: does the question-writer mean for us to rule out populations with integer values (like fruit counts)? After all, the normal distribution is a continuous distribution. I don't know; it has to do with whether you're learning the material at a high school / college / grad school level and how the normal distribution was defined to you.

 

[leena19]

I don't believe any physical value can belong to a truly normal distribution, as such a distribution allows for the possibility of arbitrary large positive and negative numbers. We can only say that the real-life distribution is approximately normal. So while a pencil diameter cannot be negative, the variance of actual pencil diameters is so small that if we fit a normal distribution to a sample, the predicted frequency of negative-diameter pencils would be effectively zero (say, 10^-50, for example). But what if part of the manufacturing process is discarding pencils that lie more than one standard deviation away from the mean? Obviously this would produce a non-normal (specifically, a truncated normal) distribution. So we have to make some assumptions and try to guess what the question-writer was looking for.

Urm...I'm having a hard time trying to understand any of the above. :(

Here's another question: does the question-writer mean for us to rule out populations with integer values (like fruit counts)? After all, the normal distribution is a continuous distribution. I don't know; it has to do with whether you're learning the material at a high school / college / grad school level and how the normal distribution was defined to you.

This question is from a local A-Level biology paper.
and all I know is that most of the biological variables conform to a normal distribution and that in a normally distributed population,about 68% fall within 1 Standard Deviation,98% within 2 SD and 100% between 3 Standard Deviations.

Also the answer to this question is 5) which means
if the ans was,
1- A,B,D would be correct
2 -A,C,D
3-A,B
4-C,D
5-Any other response or combination of responses correct,
but knowing this doesn't help much:(

 

[queenofbabes]

So you mean the answer says all 5 choices are correct? If so, I'm inclined to say that this question (and its answer) is totally rubbish.

A normal distribution will have a mean where it peaks, sort of an "expected value"

D and E are plausibly normal.
C...maybe, if they were asking for number of fruits in each tree, and if all the mango trees are the same.

I'm pretty sure A is not governed by this sort of distribution, and for B you would expect a uniform distribution within that age group, no?

 

[Borek]

C...maybe, if they were asking for number of fruits in each tree, and if all the mango trees are the same.

I think that's what they mean.

for B you would expect a uniform distribution within that age group, no?

No, there are seasonal fluctuations. For example people have more time for sex during vacations, and vacations are in Summer, so there is a peak around April/May (at least on some parts of the northern hemisphere).

 

[queenofbabes]

No, there are seasonal fluctuations. For example people have more time for sex during vacations, and vacations are in Summer, so there is a peak around April/May (at least on some parts of the northern hemisphere).

okay...

 

[Borek]

There is more to it - there are peaks like that 9 months after major power outages

 

[leena19]

So you mean the answer says all 5 choices are correct?

Sorry,for not being very clear.By answer (5) it could be any combination of responses other than those given in 1,2,3 and 4.In the sense,it could be either A,B,C,D or B,C or A,C or E or A,E & so on...

Anyway I figured out,that C) shows normal distribution and that number of fruits,number of flowers,size of fruits and seeds all come under polygenic inheritance,thus ,they all show normal distribution.It was right there in my notes.I was just looking at the wrong set(the statistics part not the note on genetics)so I guess the answers are C,D and E..