Question 1155928: Assume newborn baby weights are Normally distributed with a mean of 7.6lbs and a variance of 0.6 lbs. Find the probability a newborn baby weighs over 10lbs or below 8 lbs.
I know I have to use a z table, but I don't exactly know how
Found 2 solutions by Boreal, Edwin McCravy:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! z=(x-mean)/sd
sd is sqrt (variance) =sqrt (0.6)=0.7746
over 10 is a z> (10-7.6)/0.7746=+3.10
fewer than 8 is <(8-7.6)/0.7746=0.52
from the table or calculator 2VARS 2(normalcdf) use (3.1, 6) the 6 is large enough to be infinite.
and then get (-6,0.52) for the lower end and add the probabilities
0.0010+0.6985=0.6995
You can go to the z -table and look at the bold on the left for 3.1 and then the column for "0", with is 3.10, and the intersection of the row with 3.1 and the column with "0" has a four digit number. You want everything to the right of that up to 1. Do the same for the other, only now the number read is what you want, since it is probability from negative infinity
Answer by Edwin McCravy(20054)  (Show Source):
You can put this solution on YOUR website!
We find the z-scores for 10 pounds and for 8 pounds.
The standard deviation is the square root of the variance
The z-score for 10 pounds:
The z-score for 8 pounds:
We want to find the fraction, decimal or percent which the shaded area is
of the whole area. Notice that there is very little shading to the right
of 3.10 because there are very few babies that weigh more than 10 pounds.
In fact you can't even see anything shaded there on the graph below. But
you see 3.10 marked on the z-score axis (the horizontal axis).
There are two kinds of tables in use today. Those with both positive and
negative values in the z-column, and those that have only positive values
in the z-column.
To find the decimal fraction for the shading to the left of z=0.52:
If there are negative values in your z-column, then
find 0.5 in the z-column and go across to 0.02 and read 0.6985.
To find the decimal fraction for the shading to the right of z=3.10:
find 3.1 in the z-column and go across to 0.00 (the next column) and read
0.9990. That's the area to the left of 3.10. To find the area to the
right of 3.10 subtract from 1.0000, getting 1.0000-0.9990 = 0.0001
We add the shading left of 0.52 which is 0.6985 to the tiny shading right of
3.10, which is 0.0001 and get 0.6986.
-----------------------------
If there are only positive values in your z-column, then
find 0.5 in the z-column and go across to 0.02 and read 0.1985.
That's the shading right of z=0, so add 0.5000 to that and get 0.1985
To find the decimal fraction for the shading to the right of z=3.10:
find 3.1 in the z-column and go across to 0.00 (the next column) and read
0.4990. That's the area between z=0 and z=3.10. To find the area to the
right of 3.10 subtract from 0.5000, getting 0.5000-0.4990 = 0.0001
We add the shading left of 0.52 which is 0.6985 to the tiny shading right of
3.10, which is 0.0001 and get 0.6986.
Answer: 0.6986
But we can only expect the table to be accurate to two decimal places, so we
should only claim 0.70 as the answer.
The TI-83 or TI-84 gives more accuracy.
0.698184662
Edwin
|
|
|
