some help please with statistics (1 Viewer)

[The Spruce Moose]

yo doods if anyone here has done any statistics subject at university would be kind enough to offer some help with this question

i ahve done it several times and always get a varied answer :

A company claims that the light bulbs it manufacturers have an average life of 400 hrs and a standard deviation of 25 hrs. If the claim is true and randomly chosen batches of 100 light bulbs are tested, in what proportion of the batches will the mean life of the light bulbs be in the following range:
(i) greater than 404.5 hrs
(ii) less than 396 hrs


for some it could be a simple maths question but my mathamatical abiltities are very limited


cheers

 

[Lazarus]

http://www.maths.usyd.edu.au:8000/u/maryp/m1005/tutorials.html

Check out the q/a for tutes 5 and 6.

As melbournian pointed out, you'll need to use normal tables at some stage (should be in your textbook if you don't have them otherwise).

 

[Lazarus]

Many of us don't possess a graphics calculator. They're banned in HSC exams unless you're doing the lowest level of maths.

I can't believe you get given all those formulae during the exam! Incredible. Thanks for the table; useful.

 

[aspect]

spurce moose:

i'm assuming its normally distributed..

anyway we know mean = 400 and std dev = 25

let X be age of light bulb
i) P(X > 404.5) = P( (X - mean) / stddev > (404.5 - mean) / stddev)
= P( Z > (404.5 - 400) / 25)
= P( Z > 0.18)
= 1 - 0.5714 (from the normal distribution integral table)
= 0.4286
so approximately 43 will have a lifespan longer then 404.5

ii) P( X < 396 ) = P( Z < (396-400)/25)
= P(Z < -0.16)
= P(Z > 0.16)
= 1- 0.5636
= .4364
so approx 44 will have lifespan shorter then 396 hours

 

[aspect]

the theory on the table and fiddling with all the inequalities is too much work for me to do right now :/

 

[aspect]

well i dont have one

and we need to know the theory anyway, no graphics calcs allowed in our exams at uni

 

[aspect]

using a graphics calc means you dont need to know the theory

allows you to succeed more if you are dumb

 

[The Spruce Moose]

ye thanx laz the table turned out to be in the middle of the tex

thanx alot aspect for ur help appreciated

melbournian i dont have a graphics calcutaltor and even if i did i would not be able to use one in the examination
and as aspect said why would you want one any random joe can push bottons in a calculator
id rather understand the theory

once again thanx aspect

 

[The Spruce Moose]

yea but we are not allowed to use grphic calculators in the examination and u can still get the answer by using a graphics calculator and not understanding the full theory

just use trial and error

plus a graphics calculator costs an arm and a leg