Need help with Statistics homework

[bobfitz14]

okay so here's the question:
a. The mean time was 102.71 seconds with a standard deviation of 3.01 seconds. If the normal model is appropriate, what percent of times will be less than 99.7 seconds?

b. What is the actual percent of times less than 99.7 seconds?



this is an odd numbered question so the answer is in the back of my textbook but i want to know how to get it. the answer for A is about 16% and the answer for B is 5.7%. anyone know how??

 

[bobfitz14]

no good mathematicians here?!

 

[Signal-11]

no good mathematicians here?!

I have a degree that says I'm pretty good with statistics but I can't help you because you haven't completely stated your problem.

The answer to A will be obvious by looking in your book under the definition of standard deviation and normal distributions. B, you haven't typed out correctly.

 

[anjinha]

I love math, but I hate statistics. Sorry.

 

[AngryApple]

...
(1-phi(1))*100% = 16%
my best guess.I bet it is wrong but uh i've never been good at anything like this.
You could try Wolframalpha and see what it says.

 

[fireshot91]

From how you typed it up, isn't the answer to A and B the same thing?

 

[AngryApple]

okay so here's the question:
a. The mean time was 102.71 seconds with a standard deviation of 3.01 seconds. If the normal model is appropriate, what percent of times will be less than 99.7 seconds?

b. What is the actual percent of times less than 99.7 seconds?



this is an odd numbered question so the answer is in the back of my textbook but i want to know how to get it. the answer for A is about 16% and the answer for B is 5.7%. anyone know how??

From how you typed it up, isn't the answer to A and B the same thing?

Good point.

 

[Signal-11]

From how you typed it up, isn't the answer to A and B the same thing?

Isn't this what I said three posts up?

 

[fireshot91]

Technically, you said he didn't type B correctly. .

You can take the credit for pointing out his mistake, It's not like it matters...

 

[bobfitz14]

to those saying i didn't type it correctly i'm rereading the whole problem right now and the only thing i left out was the data list (which i don't think i need to type up nor want to cause it has 53 values).

the difference between A and B is using the Normal model or not, in A you use the Normal model but because the data doesn't follow it (supposedly) the answer should be wrong and the answer for B would be the right answer overall...haha sorry i don't know how else to explain it

 

[fireshot91]

Oh you actually have a data list. That changes things.

Can't you set up a ratio?


x/y=z/100

Where X is number of them under 99.7, and y is the total number.

You're trying to find Z.

 

[MBHockey]

So, yeah 16% makes sense for A.

I have never taken a stats course by I did a bit of it in a course in college that dealt with reliability engineering.

The normal distribution (just google image it) shows that 68% of the data will fall within 1 standard deviation of the mean (in either direction).

So your 102.71 seconds is the average, with a standard deviation of 3.01 seconds. Standard deviation is just the average of how far all the numbers in a given set are off from the average.

So what's 99.7 seconds? Conveniently, it's exactly one standard deviation below the mean. So they are just asking you, in a normal distribution, what percentage of the data falls below 1 standard deviation?

Since 68% of the data is within 1 standard deviation in both directions, that means that 34% of the data falls exactly between the mean and 1 standard deviation below the mean. since we are only talking about everything below the mean (ie, 50% of the actual data) we can just subtract 50%-34% to get 16%.

I'm a very visual person and figured it out immediately after looking at this image:

http://www.mathnstuff.com/math/spoken/here/2class/90/statpb.gif

They are asking you what percent of the lies to the left of the 34% (the one to the left of the mean).

 

[bobfitz14]

So, yeah 16% makes sense for A.

I have never taken a stats course by I did a bit of it in a course in college that dealt with reliability engineering.

The normal distribution (just google image it) shows that 68% of the data will fall within 1 standard deviation of the mean (in either direction).

So your 102.71 seconds is the average, with a standard deviation of 3.01 seconds. Standard deviation is just the average of how far all the numbers in a given set are off from the average.

So what's 99.7 seconds? Conveniently, it's exactly one standard deviation below the mean. So they are just asking you, in a normal distribution, what percentage of the data falls below 1 standard deviation?

Since 68% of the data is within 1 standard deviation in both directions, that means that 34% of the data falls exactly between the mean and 1 standard deviation below the mean. since we are only talking about everything below the mean (ie, 50% of the actual data) we can just subtract 50%-34% to get 16%.

I'm a very visual person and figured it out immediately after looking at this image:

http://www.mathnstuff.com/math/spoken/here/2class/90/statpb.gif

They are asking you what percent of the lies to the left of the 34% (the one to the left of the mean).

oh wow thank you. yeah, some of the time i get what's going on in class/for homework then other times all i can think is how the hell did i get into this class! (it's AP )

Edit: anyone know how 5.7% comes up for B? when you DON'T use the Normal model.

 

[MBHockey]

oh wow thank you. yeah, some of the time i get what's going on in class/for homework then other times all i can think is how the hell did i get into this class! (it's AP )

Edit: anyone know how 5.7% comes up for B? when you DON'T use the Normal model.

for B i believe we'd need the actual data set

 

[bobfitz14]

for B i believe we'd need the actual data set

then i guess i'll just skip that cause i have three tests tomorrow, one of which is in my Stats class, that i still need to get some last second studying in for. thanks for the help with A though!