1. ## 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.

2. ## Re: Central limit theorem

Hey Alexander. Have you learnt about confidence intervals for the mean?

3. ## Re: Central limit theorem

Do you know how to find the mean and variance of sample means?

4. ## Re: Central limit theorem

Originally Posted by Shakarri
Hey Alexander. Have you learnt about confidence intervals for the mean?
I just learn it at later of this chapter.......

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?

5. ## 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.