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R2.9 low-birth-weight babies Researchers in Norway analyzed data on the birth weights of 400,000 newborns over a 6-year period. The distribution of birth weights is Normal with a mean of 3668 grams and a standard deviation of 511 grams. 17 Babies that weigh less than 2500 grams at birth are classified as "low birth weight."

(a) What percent of babies will be identified as having low birth weight? Show your work.

(b) Find the quartiles of the birth weight distribution. Show your work.

Short Answer

Expert verified

a. The percentage of babies will be identified as having a low birth weight is 1.10%.

b. The quartiles of the birth weight distribution is:

First quartile: 3325.63grams

Third quartile: 4010.37grams

Step by step solution

01

Part(a) Step 1: Given Information

Number of newborns =400,000

Number of period=6yearperiod

Meanlocalid="1649405246193" =3668grams

Standard deviation=511grams

No. of babies weight less than localid="1649405770830" 2500grams=17babies

02

Part(a) Step 2: Explanation

Given:

=3668

=511

x=2500

The z-score is the value xdecreased by the mean, divided by the standard deviation:

localid="1649917213420" z=x-=25003668511=-2.29

Using table A: Determine the corresponding probability

localid="1649917222116" P(x<2500)=P(z<-2.29)=0.0110=1.10%

03

Part(b) Step 1: Given Information

Number of newborns=400,000

Number of periodlocalid="1649405893329" =6yearperiod

Mean=3668grams

Standard deviation=511grams

No. of babies weight less than2500grams=17babies

04

Part(b) Step 2: Explanation

Given:

=3668

=511

x=2500

The quartiles correspond with a probability of 0.25and 0.75in table A:

z=0.67

The corresponding values are then the mean multiplied by the standard deviation in addition to the z-score:

localid="1649917232279" x=-z=3668-0.67(511)=3325.63

localid="1649917237241" x=+z=3668+0.67(511)=4010.37

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