Part 1. Using the Normal Table The mean birth weight for a large sample of babie
ID: 2958965 • Letter: P
Question
Part 1. Using the Normal Table
The mean birth weight for a large sample of babies is 120 ounces with a standard deviation of 18 ounces. The birth weights follow the normal model reasonably well.
1. What percentage of babies weighs more than 140 ounces? Show your work.
2. What percentage of babies weighs less than 90 ounces? Show your work.
3. What percentage of babies weighs between 90 ounces and 140 ounces? Show your work.
4. What is the 90th percentile for birth weight? Show your work.
5. Approximately what percentage of babies weighs between 102 ounces and 138 ounces?
If possible I would appreicate work show for instance for number one I did 140-120/18 = 1.11 and the percentages.
Explanation / Answer
Given X~Normal(=120, s=18)
------------------------------------------------------------------------
(1)P(X>140) = P((X-)/S > (140-120)/18)
=P(Z>1.11)
= 0.1334 (check normal table)
--------------------------------------------------------------------------
(2) P(X<90) = P(Z<(90-120)/18)
=P(Z<-1.67)
= 0.0474(check normal table)
----------------------------------------------------------------------------
(3) P(90<X<140) = P(-1.67<Z<1.11)
= 0.819 (check normal table)
---------------------------------------------------------------------------
(4) P(X<c)=0.9
--> (Z< (c-120)/18) = 0.9
--> (c-120)/18 =1.28 (check normal table)
--> c = 120 + 18*1.28 =143.04
------------------------------------------------------------------------
(5) P(102<X<138) = P((102-120)/18 < Z< (138-120)/18)
=P(-1<Z<1)
=0.6826