When I get P(Z

Question

<Standard normal distribution> 
When I get P(Z < -1.61), how should I proceed to find the probability using table P(Z<z)?

anonymous · Answer

I was thinking 
P (Z < -1.61) = 1 - P( Z < 1.61) = xxx
Does that make sense?

dumbcow · Answer

yes that will work

dumbcow · Answer

depends on table you use
if table has neg Z values, then just look up Z=-1.61

anonymous · Answer

What if P(Z < - 51)?

dumbcow · Answer

that is essentially 0....about 99% of distribution is within 3 std dev

anonymous · Answer

I also got 0, but couldn't believe it :(
Thanks!!

dumbcow · Answer

yw

anonymous · Answer

Just to make sure I was working correctly:
$$\mu = 40$$$$\sigma^2=38.4$$$$\sqrt{n}=\sqrt{1000}$$
Find P(X<30)
$$Z = \frac{30-40}{\sigma/\sqrt{n}}=-51$$P(X<30) ~= P (Z<-51) = 1-P(51.03) = 1-1 =0?

anonymous · Answer

@dumbcow Sorry for interrupting :(

dumbcow · Answer

no prob didn't see you posted

anonymous · Answer

Could you please check to see if my work makes sense?

dumbcow · Answer

is the variance a "sample variance" ?

anonymous · Answer

I found the variance by $$\sigma^2 = npq$$

dumbcow · Answer

ok seems like it all checks out :)
due to large sample size, the Z value is very high

anonymous · Answer

Is 1000 a large sample size?

dumbcow · Answer

yes , usually anything over 50 is considered large or "significant"

anonymous · Answer

Wow! Thanks a ton!!! :)