I need help with this statistics problem, normal distributions!?

Question

I got stuck in this problem and I'm not sure how to finish it. I appreciate your help. Thanks!
A maternity hospital would like to give special treatment to babies in the lowest 3% or the highest 1% of birth weights, as they've discovered that these babies are often at risk. Birth weights in the U.S. are normally distributed with a mean of 3420 grams and a standard deviation of 495 grams. What are the specific birth weights that form the cut-offs for the lowest 3%( i.e., the 3rd percentile) and the highest 1% of newborns' weights?

Charles D · Accepted Answer

A maternity hospital would like to give special treatment to babies in the lowest 3% or the highest 1% of birth weights, as they've discovered that these babies are often at risk. Birth weights in the U.S. are normally distributed with a mean of 3420 grams and a standard deviation of 495 grams. What are the specific birth weights that form the cut-offs for the lowest 3%

Look inside a Standard Normal Distribution table for 0.03.  The corresponding z is -1.881

Then use the z-score z = (x - mu)/sigma ==>  -1.881 = ( x - 3420) /495 to find x ==> x = 2489 grams
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Highest 1% of newborns' weights?

Look inside a Standard Normal Distribution table for 0.99.  The corresponding z is +2.326

Then use the z-score z = (x - mu)/sigma ==>  +2.326 = ( x - 3420) /495 to find x ==> x = 4571 grams

Then look in a  (SND) table for the

JiN · Answer

You should sketch the graph, it would be clearer that way. Anyway, provided that the distribution is truly normal (which is stated in the question), the following should hold true :

1. 68% of the data should deviate +/- 1 standard deviation from the mean. i.e., 68% of the population's weight ranges from 2925g (mean - 1s.d.) to 3915g (mean + 1s.d.).

2. 95% of the data should deviate +/- 2 standard deviation from the mean, i.e. 95% of the population;s weight ranges from 2430g (mean - 2s.d.) to 4,410g (mean + 2s.d.) Taking only the lower end, (~2.5%, close enough to 3%), would be the babies weighing less than 2430g. That would be your first answer.

3. 99.7% of the data should deviate +/- 3 standard deviation from the mean, which would give a range of 1935g to 4905g. You can approximate the highest 1% to be babies with weight exceeding 4905g. 

Of course, if you want to be exact,you could make a simple ratio approximation from 2s.d. to 3s.d., assuming that as the curve tapers off, the curve is similar to a straight line. I'll leave that exercise to you, hopefully it's not that difficult for you to get.

I need help with this statistics problem, normal distributions!?

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