exam1

(90-112)/6.8

1c

pnorm(125, 112, 6.8)-pnorm(90, 112, 6.8)

## [1] 0.9714392

1d

qnorm(.95, 112, 6.8)

## [1] 123.185

3b

(.12*.97)+(.88*.355)

## [1] 0.4288

3c

(.12*.97)/.429

## [1] 0.2713287

4a

sqrt(.4*(1-.08))

## [1] 0.60663

4b

dbinom(0, 5, .08)

## [1] 0.6590815

dbinom(1, 5, .08)

## [1] 0.2865572

dbinom(2, 5, .08)

## [1] 0.04983603

dbinom(3, 5, .08)

## [1] 0.004333568

dbinom(4, 5, .08)

## [1] 0.000188416

dbinom(5, 5, .08)

## [1] 3.2768e-06

4c

pbinom(2, 5, .08)

## [1] 0.9954747

1-pbinom(3, 5, .08)

## [1] 0.0001916928

5a

flu <- c(35, 41, 55, 65, 29, 60, 49, 24, 37, 110, 28, 40, 47, 58, 30, 37,15, 50, 28)

hist(flu)

mean(flu)

## [1] 44.10526

sd(flu)

## [1] 20.84038

q1 <- quantile(flu, prob=.25)
q3 <- quantile(flu, prob = .75)

IQR <- q3-q1

q3+(1.5*IQR)

## 75% 
##  87

6a

sqrt(160*(1-.16))

## [1] 11.5931

dbinom(20, 100, .16)

## [1] 0.05674059

6b

pnorm(20.5, 20, 11.593)-pnorm(19.5, 20, 11.593)

## [1] 0.03440168

7b

400/sqrt(50)

## [1] 56.56854

pnorm(2900, 3000, 56.569)

## [1] 0.03855113

6c

sqrt((.16*.84)/100)

## [1] 0.03666061

pnorm(.165, .16, 0.037)-pnorm(.155, .16, .037)

## [1] 0.107495