Grace L.

asked • 04/22/18

normal distribution with a mean, standard deviation

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?

1 Expert Answer

By:

Thomas R. answered • 04/22/18

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

Grace L.

Thank you so much!! I totally understand that one now. Could you perhaps help me with this one as well?
 
The average height of adult males is 70 inches with a standard deviation of 2.4 inches. If the heights are normally distributed, how high should a doorway be such that 95% of all men can pass through the doorway without hitting their heads
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04/22/18

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

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