6. A real number is said to be "normal" if, when written in any basc b, the digits 0,1,2,...,b-1 all appear with oqual f

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6 A Real Number Is Said To Be Normal If When Written In Any Basc B The Digits 0 1 2 B 1 All Appear With Oqual F 1 (124.98 KiB) Viewed 18 times

6. A real number is said to be "normal" if, when written in any basc b, the digits 0,1,2,...,b-1 all appear with oqual frequency. That is, there should be an equal proportion of Os, and Is, and 2s, etc. One of the strangest results in mathematics is this: It can be shown that nearly all real numbers are normal, and yet, proving any particular number is normal is very difficult. Indeed, mathematicians do not know if or care normal! On Canvas/TritonEd, you can find the file pibinary.csv which contains the first 10242 digits of pi in binary (base 2). Notice it starts with 11, which means 3 in binary. If y really is normal, what per- centage of Is do you expect in its binary expansion? Assuming the first 10242 digits are representative of all of t, conduct a hypothesis test on the proportion of ls in by randomly selecting 314 digits without replacement. You should set up variable(s) and hypotheses, write code to select the digits and get the sample proportion, draw a picture of a sampling distribution, shade an arca, calculate a P-value, and reach a conclusion about your hypotheses using a= 0.05.