## xEnOnn Group Title A population of normally distributed account balances have mean balance $150 and standard deviation of$35. What is the probability that the total balance for a random sample of 40 accounts will exceed $6400? 2 years ago 2 years ago • This Question is Closed 1. campbell_st Group Title find the average balance for the 40... 6400/40 =$160 this means that the average balance of the 40 selected exceeds $160 2. DBhatta Group Title X~N(150,35) X= Total balance / 40 X= 6400/40 X = 160 P(X>160) = ? =P(Z>(1600-150)/35) =P(Z>0.285) = 1- P(z<0.285) =1 - 0.6122 = 0.3878 3. campbell_st Group Title using a z score $z =(x - \mu)/\sigma$ $z = (160 - 150)/35$ z = 0.2857 4. xEnOnn Group Title Thanks! hmm...actually, I have also calculated both the different answers by @DBhatta and @campbell_st. And that's why I am not sure what the correct answer should be. hahaha... 5. campbell_st Group Title I would have thought that if the balance is to exceed then its the probability should be between 50% and 68%... as the average is greater than the mean... and the z score is 0.2857 6. DBhatta Group Title I'm pretty sure with my answer and @campbell_st also has the same answer. He has just stopped after calculating z and I've calculated until the end. 7. DBhatta Group Title @campbell_st actually it should be below 50% |dw:1335172829891:dw| 8. xEnOnn Group Title oh no...wait, so sorry, I saw the wrong numbers. Yes, @campbell_st and$DBhatta both has the same answer. Actually, here's what I got for my other answer: $\frac { 160-150 }{ \frac { 35 }{ \sqrt { 40 } } } =1.807$

9. xEnOnn Group Title

I don't know which is the right way to look at this problem.

10. campbell_st Group Title

DBhatta's graph sums it up

11. DBhatta Group Title

@xEnOnn are you using z test or normal distribution? The question asks about normal distribution.

12. xEnOnn Group Title

oh, is what I have done a z-test instead of a normal distribution?

13. DBhatta Group Title

yes my friend. It should be normal distribution $z = x - u / \sigma$

14. xEnOnn Group Title

But it has that 40 accounts info, isn't that n=40?

15. DBhatta Group Title

ah...let me see. it's becoming more interesting now.

16. xEnOnn Group Title

haha...okay, thanks!

17. DBhatta Group Title

oh yes, it's z-distribution.

18. xEnOnn Group Title

oh so we should use the other method? The one I written just now? But why?

19. DBhatta Group Title

Yes use the one you have written. We are assuming that population mean is equal to the sample mean.

20. xEnOnn Group Title

oh I see...Thanks for you help!! :)

21. DBhatta Group Title

Actually you helped me, I was off-track. It was you who made me realize. :)