# Central limit theorem

• Aug 13th 2013, 09:42 AM
alexander9408
Central limit theorem
The standard deviation of the masses of fish in a large population is 4.55kg. If random samples of size 50 are drawn from this population, find the probability that the sample mean differs from the population mean by less than 0.8kg.
• Aug 13th 2013, 10:58 AM
Shakarri
Re: Central limit theorem
Hey Alexander. Have you learnt about confidence intervals for the mean?
• Aug 14th 2013, 09:08 AM
Lord Voldemort
Re: Central limit theorem
Do you know how to find the mean and variance of sample means?
• Aug 17th 2013, 05:19 AM
alexander9408
Re: Central limit theorem
Quote:

Originally Posted by Shakarri
Hey Alexander. Have you learnt about confidence intervals for the mean?

I just learn it at later of this chapter.......

Quote:

Originally Posted by Lord Voldemort
Do you know how to find the mean and variance of sample means?

Yes

This is how I solve this question:
X ̅~N(x ̅,〖4.55〗^2/50)
P(x ̅-μ<0.8) and I got 0.893 as my final answer, is that correct?
• Aug 17th 2013, 10:11 AM
Lord Voldemort
Re: Central limit theorem
You're close. Remember that the question asks the probability that the sample mean differs by less than .8 kg - this means you want the confidence level, not the left tailed p value (which is what you calculated, .8925). Take the answer you got and remove the left tail and you'll have the correct answer.
• Aug 20th 2013, 09:16 PM
parex
Re: Central limit theorem