## Assistance with probability problems before exam

Hello,

I am a student in International Trade and I have a Statistical exam tomorrow (in 12 hours to be precise). I would really need your help and assistance to resolve this exercise as I am really tired and this is my last exam.

The exercise goes like this :

In a shop customers spend an amount of money Y ~ N (6.3, 2.56) and 35% of the customers buy fruits. During one morning there are 35 clients in the shop.
1) Let X denote the number of clients that buy fruits.
Find µ = EX and σ² = Var(X) and verify the property of Chebyshev.

2) Let Y(1), Y(2), ..., Y(35) denote the amounts of money they spend un the hop and let S(35) denote the total amount of money they spend, Y(bar) the mean amount of money and s² the sample variance.
a) Find P(S(35) < 208), P(S(35) = 224.2), P(215 < S35 <= 230)
b) Find P(X(bar) => 6.51)
c) Find a 95% c.u.b for Y(bar)
d) Find P(s² <= 2.45)
e) Find a 90% c.l.b for s²

I am willing to work on this and I would love some guidance on how to begin. But please consider that I have limited time.

Your help is much appreciated ! Thank you