Question

In: Math

The numbers 1,6,15,20,15,6,1 are the coefficients of the binominal expansion (p+q)^6. Use the normal quantile plot...

The numbers 1,6,15,20,15,6,1 are the coefficients of the binominal expansion (p+q)^6. Use the normal quantile plot method to show that these numbers are close to a normal distribution.

Solutions

Expert Solution

first sort the values in ascending order

1
1
6
6
15
15
20

here we have 7 values so divide the standard normal distribution into 8 equal-sized areas with 7 values. so each segment has 12.5% area

find z values for each of the segment

probability z values
12.5 0.125 -1.15035
25 0.25 -0.67449
37.5 0.375 -0.31864
50 0.5 -1.4E-16
62.5 0.625 0.318639
75 0.75 0.67449
87.5 0.875 1.150349

i have used excel to find out z scores(NORMSINV)

now plot the graph with the following values

actual quantiles theoretical quantiles
1 -1.15034938
1 -0.67448975
6 -0.318639364
6 -1.39214E-16
15 0.318639364
15 0.67448975
20 1.15034938

here R-value is 0.916. straight line is good fit for data

straight line on q q plot indicates the data is approximately normal.

The numbers 1,6,15,20,15,6,1 are close to a normal distribution.

remark:i have used excel to draw the graph


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