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?

Question

campbell_st · Answer

find the average balance for the 40... 

6400/40 = $160

this means that the average balance of the 40 selected exceeds 

$160

anonymous · Answer

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

campbell_st · Answer

using a z score

$$z =(x - \mu)/\sigma$$

$$z = (160 - 150)/35$$

z = 0.2857

anonymous · Answer

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...

campbell_st · Answer

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

anonymous · Answer

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.

anonymous · Answer

@campbell_st actually it should be below 50% |dw:1335172829891:dw|