Thread: Probability to X-score

I'm still working with:

"A region's population is 7,800, per capita income approximately observes normal distribution with mean $12,100 and standard deviation $6,050."

Above what income level in dollars do the richest 5% of the region's population earn?

So since 0.4500 is between 1.64 and 1.65 in my table, I choose 1.645 to be my z-score. ( I still don't understand why this is?)

0.4500 = 1.645
1.645=(X-12100) / 6050
9952.25= X - 12100
X= 22052.25

I feel this is the right answer, but for some reason I can't ever figure out the proper notations to include in my problem solving process so that I get full marks. If I just write down what I did up there, is that "proper"?

Originally Posted by peanutbutter

I'm still working with:

"A region's population is 7,800, per capita income approximately observes normal distribution with mean $12,100 and standard deviation $6,050."

Above what income level in dollars do the richest 5% of the region's population earn?

So since 0.4500 is between 1.64 and 1.65 in my table, I choose 1.645 to be my z-score. ( I still don't understand why this is?)

0.4500 = 1.645
1.645=(X-12100) / 6050
9952.25= X - 12100
X= 22052.25

I feel this is the right answer, but for some reason I can't ever figure out the proper notations to include in my problem solving process so that I get full marks. If I just write down what I did up there, is that "proper"?

Your answer is correct, but probably too accurate compared to the accuracy of your tables ...... I'm not your professor but I'd be more comfortable with a rounded answer of $22050 given the accuracy of your tables .....

You might want to include an opening statement in your solution:

You're looking for the value of x* such that Pr(X > x*) = 0.05.
This in turn means finding a value z* of Z such that Pr(Z > z*) = 0.05.

And your final answer should be given in units of money: $22,050 (if you round like I did).