normal distribution with a mean, standard deviation

Question

If the weight of female high school students closely follows the normal distribution with a mean of 125 pounds and a standard deviation of 5 pounds, what range of weights includes the middle 80% of the girls in high school?

Answer 1

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