Thomas R. answered • 04/22/18

A.S. in Mathematics, over 25 years math tutoring plus 8 in Accuplacer

Grace:

It sometimes seems tough at first, but once you get it, this becomes easy. Remember the Z-score formula:

Z = X - μ ?

S

If you solve it for X instead by cross-multiplying and then isolating X, you get:

X = μ + SZ , which is the formula you need. You already know:

μ = 125

S = 5

but you have to find Z. I have seen a wide variety of structures for Z (normal score) tables, so I can't say for sure how yours is shaped. If you look up either 0.4 at the center of the table (my book) or .1 (if your book lists everything as left tails, since .5 - .4 = .1 in the tail). Either way, you get Z = 1.28, and it is + / -- 1.28 since you want 40% above and 40% below the middle.

Plug in everything and you get

X = 125 - 1.28 (5) = 118.6 and X = 125 + 1.28 (5) = 131.4

Thomas R.

Okay, I'm pleased that you feel better about the question. And yes, I will help you with this one as well.

This sort of question feels confusing at first, doesn't it? Actually, it's very much like the last one. If the lowest 95% of all men can pass through the doorway, you need only find out separates the top 5% from the 45% near the center (or if you have one of those left-tail tables, you'll look up an area of .9500). Either way, you will see that the correct Z-score seems to be a coin-toss between 1.64 and 1.65. When it is

*exactly*halfway between two values, we average them and get:Z = 1.645 You already know that

μ = 70 and:

S = 2.4 so you can plug them into the same formula as last time:

X = μ + SZ to get the final answer.

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04/23/18

Grace L.

04/22/18