Mean and s.d of normal distribution? (The time taken for a randomly chosen student to complete the test is...)

[apple2357]

Any stats experts out there who can help me with this question?

For anyone familiar it looks like a fairly common question where you are given two bits of information and use it to find the mean and s.d.
So its easy enough to interpret the second bit ( 1 in 8 take less than 35 minutes) and construct an equation but how do we make sense of the condition containing the 38 and 41?

No need to do the question, i just want help with interpretation of the statement '4 in 5 students take less than 38 or more than 41 mins'

 

[Dr.Peterson]

Any stats experts out there who can help me with this question?

For anyone familiar it looks like a fairly common question where you are given two bits of information and use it to find the mean and s.d.
So its easy enough to interpret the second bit ( 1 in 8 take less than 35 minutes) and construct an equation but how do we make sense of the condition containing the 38 and 41?

No need to do the question, i just want help with interpretation of the statement '4 in 5 students take less than 38 or more than 41 mins'
View attachment 37127

It says the area under the normal curve between x=38 and x=41 is 0.2. Do you see why?

 

[apple2357]

Maybe but not sure how you would use that in this question. What z value would you use?

 

[Dr.Peterson]

Maybe but not sure how you would use that in this question. What z value would you use?

I don't know what to do next. I'm not sure this can be solved algebraically. Where did the problem come from, and what topic is it related to? Is some sort of software allowed?

 

[apple2357]

The question appeared in a book that was sent to me online from a teacher friend of a friend. Don't know much more about it i am afraid. But i can't see a way of doing it except maybe interpreting the statement so we can ignore then X>41 bit because sigma might be small enough.
The topic is inverse normal distribution problems - the natural extension that usually follows after having learnt to standardise and work out probabilities. Feels like a old question and is worth 4 marks, i don't think software is the route but not sure how that would help anyway??

 

[apple2357]

Anyway, thanks for your help. I wanted some reassurance that i wasn't going mad. No need to ponder much more on it.

 

[blamocur]

I don't know what to do next. I'm not sure this can be solved algebraically. Where did the problem come from, and what topic is it related to? Is some sort of software allowed?

My quick and dirty (and potentially buggy) script produced [imath]\mu \approx 36.740[/imath] and [imath]\sigma \approx 1.513[/imath] -- feel free to double-check. BTW, the condition [imath]\sigma < 2[/imath] is needed to make the solution unique.

 

[apple2357]

My quick and dirty (and potentially buggy) script produced [imath]\mu \approx 36.740[/imath] and [imath]\sigma \approx 1.513[/imath] -- feel free to double-check. BTW, the condition [imath]\sigma < 2[/imath] is needed to make the solution unique.

Thank you, please explain more! in particular the uniqueness of the solutiion..

 

[Dr.Peterson]

My quick and dirty (and potentially buggy) script produced [imath]\mu \approx 36.740[/imath] and [imath]\sigma \approx 1.513[/imath] -- feel free to double-check. BTW, the condition [imath]\sigma < 2[/imath] is needed to make the solution unique.

I tried solving this using Excel solver, and confirmed your solution, but could only get to that solution by carefully choosing my starting values. I don't have much experience using Solver, so I don't know how to make it work better.

But it's possible that something like this is what was intended. I'd like to see exactly what the book said in the context of the problem.

 

[apple2357]

I tried solving this using Excel solver, and confirmed your solution, but could only get to that solution by carefully choosing my starting values. I don't have much experience using Solver, so I don't know how to make it work better.

But it's possible that something like this is what was intended. I'd like to see exactly what the book said in the context of the problem.

I will see if i can get hold of more details.

 

[blamocur]

Thank you, please explain more! in particular the uniqueness of the solutiion..

There is not much to explain there. I've simply noticed from a graph that there is more than one solution in my numeric approach, but only one satisfying the restriction.