Data 605 Discussion 9

2. Let S200 be the number of heads that turn up in 200 tosses of a fair coin. Estimate

\(\ 1/√2π*e^(−1/2)\)

e=2.71828
clt=1/sqrt(2*pi)* (e**(-1/2))

1. \(\ P(S200 = 100)\)

n=200
p=1/2
q=1/2

n*p

## [1] 100

ans=sqrt(n*p*q)
x100=(100-(n*p))/ans
x100

## [1] 0

x100*clt

## [1] 0

2. \(\ P(S200 = 90)\)

n=200
p=1/2
q=1/2

n*p

## [1] 100

ans=sqrt(n*p*q)
x90=(90-(n*p))/ans
x90

## [1] -1.414214

x90*clt

## [1] -0.3421984

3. \(\ P(S200 = 80)\)

n=200
p=1/2
q=1/2

n*p

## [1] 100

ans=sqrt(n*p*q)
x80=(80-(n*p))/ans
x80

## [1] -2.828427

x80*clt

## [1] -0.6843968