Statistics problem on basic statistics

[shanshayan]

I need answer of thees question

The amount of money saving accounts at BOC bank at the end of april 2010 had mean of R.s 3460 with a standard diviation R.s 550

1.if it is assumed that these bank balances are normally distributed find the probability that a single randomly chosen account had more than R.s 4000 in it at the end of april

2.if a simple random sample of 100 account is selected ans the mean balance at the end of april calculated what is the probability that this mean exceeds R.s 3500?

3.in using the normal distribution to answer part 2 it was not necessary to make the assumption that the individual balances are normally distributed Briefly explain Why?Z=X-μ/σ

=4000-3460/550
=540/550
=0.9818

z for 0.98=0.8365

i can't calculate probability ,part 2 and part 3

 

[mfb]

Is 0.8365 your answer to (1)? This cannot be right - the probability to have a value above the mean (3460) is 0.5, the probability to have more than 4000 cannot be larger than that.

For (2), how does the distribution of the mean look like? There is a nice formula, but you can derive it yourself with errror propagation as well.

(3): Which special properties of the normal distribution do you know?