Mean, deviation and normal curve

[HeatherReed]

Assume that 58.3% of grade 11 students have heights between 1.6m and 1.9m and the data are normally distributed.
A. Find the mean B. Find the standard deviation C. Draw the corresponding normal curve

 

[BigBeachBanana]

[math]\Pr\left(\frac{1.6-\mu}{\sigma}\le Z\le\frac{1.9-\mu}{\sigma}\right)=58.3\%[/math]

 

[blamocur]

Unless I am missing something here the problem has an infinite number of solutions, including these five pairs of means and standard deviations:
1.886 0.067
1.819 0.171
1.755 0.185
1.692 0.175
1.632 0.126
The corresponding graphs for the above pairs all have roughly the same integrals:

 

[JeffM]

I am asking a question here. If there are finite boundaries on the possible values, can the distribution even be a normal distribution? Are there some students more than 100 meters tall? Any fewer than 0 meters tall?

 

[Harry_the_cat]

Is that the entire question word for word? If so, as blamocur said, there are an infinite number of solutions.

 

[JeffM]

Is that the entire question word for word? If so, as blamocur said, there are an infinite number of solutions.

My dear feline,

You know that no poster ever reads the guidelines, which say to post the complete and exact statement of the problem. Posters infinitely prefer to post their own interpretation of the problem, which interpretation often is the source of the poster’s confusion. For example, I suspect the problem says “approximately normal” or some such similar qualification that takes us out of the realm of integrals completely.

Of course, it may be a badly worded problem that posits people with negative heights (presumably living in Australia, where gravity is backwards and things fall northward).

I suggest you have a bowl of cream flavored with catnip as alcohol is bad for cats. When I read questions like this, I head to the liquor cabinet as catnip has never done much for me.

 

[Deleted member 4993]

I

My dear feline,

You know that no poster ever reads the guidelines, which say to post the complete and exact statement of the problem. Posters infinitely prefer to post their own interpretation of the problem, which interpretation often is the source of the poster’s confusion. For example, I suspect the problem says “approximately normal” or some such similar qualification that takes us out of the realm of integrals completely.

Of course, it may be a badly worded problem that posits people with negative heights (presumably living in Australia, where gravity is backwards and things fall northward).

I suggest you have a bowl of cream flavored with catnip as alcohol is bad for cats. When I read questions like this, I head to the liquor cabinet as catnip has never done much for me.

What about me - firewater is no good for me !!

 

[Harry_the_cat]

My dear JeffM,

Even if the question said "approximately normal", it is still not possible to calculate the mean from the info given. Are we to assume that the 58.3% quoted are spread evenly around the mean? And why would we assume that?

I agree most people would say "what guidelines?"

Also, regarding gravity down under - things still fall down when I knock them off the table. Methinks you have your globe upside down - what's the right way up anyway? Also, my preferred drink is a Cheshire Cat Cocktail - none of this catnip rubbish for me!

Cheers!

 

[JeffM]

My dear JeffM,

Even if the question said "approximately normal", it is still not possible to calculate the mean from the info given. Are we to assume that the 58.3% quoted are spread evenly around the mean? And why would we assume that?

I agree most people would say "what guidelines?"

Also, regarding gravity down under - things still fall down when I knock them off the table. Methinks you have your globe upside down - what's the right way up anyway? Also, my preferred drink is a Cheshire Cat Cocktail - none of this catnip rubbish for me!

Cheers!

I suspect that if we knew what the problem said, we might have a clue.