DATA 605 FUNDAMENTALS OF COMPUTATIONAL MATHEMATICS

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10 Find the probability that among 10,000 random digits the digit 3 appears not more than 931 times

\(P(X <= 931 | pi = .1) = 0.01064763\)

n <- 10000
pi <- .1
x <- 931

pbinom(x, n, pi)

## [1] 0.01064763

12 A balanced coin is flipped 400 times. Determine the number x such that the probability that the number of heads is between 200 - x and 200 + x is approximately .80.

\(P(200 - x < X < 200 + x | pi = .5) = 0.8\)

n <- 400
pi <- .5
given <- .8
#we want the 10th percentile on both sides of the distribution
pctile <- (1 - given)/2

a <- qbinom(pctile, n, pi)

(x <- 200 - a)

## [1] 13

DATA 605 FUNDAMENTALS OF COMPUTATIONAL MATHEMATICS

Discussion W9: 9.1 #10 & #12

Kyle Gilde

10/18/2017

10 Find the probability that among 10,000 random digits the digit 3 appears not more than 931 times

12 A balanced coin is flipped 400 times. Determine the number x such that the probability that the number of heads is between 200 - x and 200 + x is approximately .80.