Stat HW: Xbar and sampling infinite populations

[Hip2dagame]

Homework Statement

Two problems:
1) We're given a probability distribution function with possible values and their probabilities of occurring:

X=1, P = .67
X=2, P = .19
X=3, P = .05
X=4, P = .04
X=5, P = .03
X=6, P = .02

And we need to find P(XBAR >=6) and P(XBAR >=5). I don't get this XBAR business...

2) Use Central Limit Theorem. Infinite population. 25% of the pop has the value 1, 25% 2, 25% 3, and 25% 4. What is the pop mean, pop std dev, sample mean, and sample std dev?

Homework Equations

1) I found that mu = E(X) = 1.69, variance = 1.494, std dev = 1.222, so mu of XBAR = 1.69 too, and std dev XBAR = stddev/(sqrt(n)) = .5

So I figure you must need to get the Z statistic for XBAR, right? That must mean

P(Xbar >=6) =

P(x=6) =

(Xbar - mu of XBAR)/(stddev of XBAR) =

6 - 1.69/.5

however, this value is too big for the Z / normal distribution table I've been given. What do I do about the Xbar crap?

Same for the XBAR >= 5, the Z value is too big...

2) The pop and sample mean are both 2.5, but shouldn't the std dev for an infinite pop be 0?

The Attempt at a Solution

See above.

Thanks.

 

[SteamKing]

xbar is the mean value of x (when printed, the x has a horizontal bar on top)

 

[Hip2dagame]

^No, because the mean (as I calculated) is 1.69. That's clearly always lower than 6 or 5.

Anyone else?