Normal Distribution and Significance Level

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Math 221
Week 6 Lab

Submitted by: Merima Ceric

Part 1. Normal Distributions and Birth Weights in America

1) What percent of the babies born with each gestation period have a low birth weight (under 5.5 pounds)? a) Under 28 = 99.88%
The NORMDIST formula was used to calculate: =NORMDIST(5.5,1.88,1.99,True) X= 5.5
Mean= 1.88
Standard Deviation=1.19

b) 32 to 35 weeks = 43.83%
The NORMDIST formula was used to calculate: =NORMDIST (5.5,5.73,1.48,True) X= 5.5
Mean= 5.73
Standard Deviation=1.48

c) 37 to 39 weeks = 4.66%
The NORMDIST formula was used to calculate: =NORMDIST(5.5,7.33,1.09, True) X= 5.5
Mean= 7.33
Standard Deviation=1.09

d) 42 weeks and over = 2.75%
The NORMDIST formula was used to calculate:=NORMDIST( 5.5, 7.65,1.12, True) X= 5.5
Mean= 7.65
Standard Deviation=1.12

2) Describe the weights of the top 10% of the babies born with each gestation period.

a) 37 to 39 weeks = 8.73 lbs
The NORMINV formula was used to calculate: =NORMINV(0.9,7.33,1.09) Probability= 0.9
Mean=7.33
Standard Deviation= 1.09
b) 42 weeks and over= 9.09 lbs
The NORMINV formula was used to calculate: =NORMINV(0.9,7.65,1.12) Probability= 0.9
Mean=7.65
Standard Deviation= 1.12

3) For each gestation period, what is the probability that a baby will weigh between 6 and 9 pounds at birth? a) 32 to 35 weeks = 41.40%
The NORMDIST formula was used to calculate:
= NORMDIST(9,5.73,1.48,TRUE)-NORMDIST(6,5.73,1.48,TRUE) x= 9x=6
mean= 5.73mean = 5.73
standard deviation= 1.48standard deviation= 1.48

b) 37 to 39 weeks = 82.61%
The NORMDIST formula was used to calculate:
= NORMDIST(9,7.33,1.09,TRUE)-NORMDIST(6,7.33,1.09,TRUE) x= 9x=6
mean= 7.33mean = 7.33
standard deviation= 1.09standard deviation= 1.09

c) 42 weeks and over = 81.57%
The NORMDIST formula was used to calculate:
= NORMDIST(9,7.65,1.12,TRUE)-NORMDIST(6,7.65,1.12,TRUE) x= 9x=6
mean= 7.65mean = 7.65
standard deviation= 1.12standard deviation= 1.12

4) A birth weight of less than 3.3 pounds is classified by the NCHS as a “very low birth weight.” What is the probability that a baby has a very low birth weight for each gestation period.

a) under 28 weeks = 88.36%
The NORMDIST formula was used to calculate:
= NORMDIST( 3.3,1.88,1.19,true)
x= 3.3
mean= 1.88
standard deviation = 1.19

b) 32 to 35 weeks = 5.03%
The NORMDIST formula was used to calculate: = NORMDIST( 3.3,5.73,1.48,true)
x= 3.3
mean= 5.73
standard deviation = 1.48

c) 37 to 39 weeks = 0.01%
The NORMDIST formula was used to calculate: = NORMDIST( 3.3,7.33,1.09,true)
x= 3.3
mean= 7.33
standard deviation = 1.09

Part 2. Age Distribution in the United States

1) Mean = 36.48
The Mean was found by using the SUM formula
=SUM of mid*relfreq
Age | Midpoint| Relative Frequency| mid*relfreq| mid^2*relfreq| 0 - 4| 2| 6.7%| 0.134| 0.268|
5 - 9| 7| 6.8%| 0.476| 3.332|
10 - 14| 12| 7.4%| 0.888| 10.656|
15 - 19| 17| 7.2%| 1.224| 20.808|
20 - 24| 22| 7.0%| 1.54| 33.88|
25 - 29| 27| 6.2%| 1.674| 45.198|
30 - 34| 32| 6.8%| 2.176| 69.632|
35 - 39| 37| 7.3%| 2.701| 99.937|
40 - 44| 42| 8.1%| 3.402| 142.884|
45 - 49| 47| 7.6%| 3.572| 167.884|
50 - 54| 52| 6.6%| 3.432| 178.464|
55 - 59| 57| 5.5%| 3.135| 178.695|
60 - 64| 62| 4.2%| 2.604| 161.448|
65 - 69| 67| 3.4%| 2.278| 152.626|
70 - 74| 72| 3.0%| 2.16|...
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