Calculating Probability for Mean Shift in 1992: Help and Tips (Urgent)

[bayan]

hey everyone.

I have a question that I cannot seem to work the answer for.

the question is.

between 1983-1991 X ~ N (20744,8 xxx xxx) Cant exactly remember the numbers, but how do I get the probability that in 1992 the mean will be at least 21000?

I have calculated the $$Z$$ value which was about$$-7.5$$

will the $$Z$$ value be the same for the year 1992?

and also the term at least 21000 confusex me.

any help would be gratly appriciated as I have to do a similar one tomarrow in my test

 

[bayan]

anyone? I really need help with this

 

[HallsofIvy]

I have no idea what the question is!

Apparently, between 1983 and 1999 something was normally distributed with mean 20744 and some standard deviation. You are asking how to find the probability that the mean (of a sample?) is a at least 21000?
Convert from the given distribution to the standard normal distribution.
What "z" does 21000 convert to? Most tables give probability for z between the number and 0. To find probability for z greater subtract that from 1/2.

 

[bayan]

the X value in this case would be 9 wouldn't it?
also I got $$Z=-7.5$$ for the first data and I got $$Z=-7.63$$ for mean being grater than 21000 :(

I know my Z value is wrong, But I don't know where I made the mistake

$$Z=\frac{9-21000}{2750}$$

$$Z= -7.63$$

Can you please see where I have made a mistake

thank you

 

[EnumaElish]

the X value in this case would be 9 wouldn't it?

1991 - 1983 + 1 = 9. But I thought X is a random var. and not the year. You need to be clear about how X relates to the year.