Question

In: Math

0-499 22 500-999 201 1000-1499 1,645 1500-1999 9,365 2000-2499 92,191 2500-2999 569,319 3000-3499 1,387,335 3500-3999 988,011...

0-499 22
500-999 201
1000-1499 1,645
1500-1999 9,365
2000-2499 92,191
2500-2999 569,319
3000-3499 1,387,335
3500-3999 988,011
4000-4499 255,700
4500-4999 36,766
5000-5499 3,994
0-499 22
500-999 201
1000-1499 1,645
1500-1999 9,365
2000-2499 92,191
2500-2999 569,319
3000-3499 1,387,335
3500-3999 988,011
4000-4499 255,700
4500-4999 36,766
5000-5499 3,994

D) Use the normal model to determine the proportion of babies in each class

How do I manually determine the normal mode? Please provide step by step manually (excel is what I am using, however I need to show steps.

Thank you.

Solutions

Expert Solution

Class limit Frequency (f) Mid value (x) xf x^2f
0-499 22 249.5 5489 1369505.5
500-999 201 749.5 150649.5 112911800.3
1000-1499 1,645 1249.5 2055427.5 2568256661
1500-1999 9,365 1749.5 16384067.5 28663926091
2000-2499 92,191 2249.5 207383654.5 4.6651E+11
2500-2999 569,319 2749.5 1565342591 4.30391E+12
3000-3499 1,387,335 3249.5 4508145083 1.46492E+13
3500-3999 988,011 3749.5 3704547245 1.38902E+13
4000-4499 255,700 4249.5 1086597150 4.61749E+12
4500-4999 36,766 4749.5 174620117 8.29358E+11
5000-5499 3,994 5249.5 20966503 1.10064E+11
Sum= 3344549 11286197976 3.88981E+13
Average= 3374.505195 11630297.32
Mean (M)= 3374.5052
Standard deviation (S)= 492.9625

Class limit Frequency (f) x* z=(x*-M)/S T Proportion
0 -6.8454 0 0
0-499 22 499.5 -5.8321 0 0
500-999 201 999.5 -4.8178 0 0
1000-1499 1,645 1499.5 -3.8035 0.0001 0.0001
1500-1999 9,365 1999.5 -2.7893 0.0026 0.0025
2000-2499 92,191 2499.5 -1.775 0.0379 0.0353
2500-2999 569,319 2999.5 -0.7607 0.2234 0.1855
3000-3499 1,387,335 3499.5 0.2536 0.6001 0.3767
3500-3999 988,011 3999.5 1.2678 0.8976 0.2975
4000-4499 255,700 4499.5 2.2821 0.9888 0.0912
4500-4999 36,766 4999.5 3.2964 0.9995 0.0107
5000-5499 3,994 5499.5 4.3107 1 0.0005
Mean (M)= 3374.5052
Standard deviation (S)= 492.9625

Since for normal distribution mean=mode, hence mode=3374.5052.


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