Assignment3

rm(list=ls()) # remove all objects from environment cat() # Clear the console graphics.off() # Clear all graphs gc() # Clear unused memory

#question 1

round(sum (dbinom(x = 9:12,
       size = 20,
       prob = .5)),digit = 4)

## [1] 0.6167

#Question 2

round(sum (dbinom(x = 4:5,
       size = 13,
       prob = .2)),digit = 4)

## [1] 0.2226

#Question 3

ppois(q = 3,
      lambda = 4.2,
      lower.tail = TRUE,
  
)

## [1] 0.3954034

#Question 4

phyper(q = 1,
       m = 6,
       n = 11,
       k = 3,
       lower.tail = T
  
)

## [1] 0.7279412

#Q5

phyper(q = 1,
       m = 6,
       n = 19,
       k = 6, 
       lower.tail = F 
) 

## [1] 0.4528515

#Q6

print(sqrt(90000))

## [1] 300

#300

round(pnorm(q = 1460,
      mean = 800,
      sd = 300
  
) - pnorm(q = 1040,
          mean = 800,
          sd = 300
  
), digits = 4)

## [1] 0.198

#Q7

round(pnorm(q = 111,
            mean = 106,
            sd = 4
            ) - pnorm(q = 103,
                      mean = 106,
                      sd = 4), digits = 4
      )

## [1] 0.6677

#Q8

round(qnorm(p = .03,
            mean = 3.34,
            sd = .07
            ), digits = 2) 

## [1] 3.21

round(qnorm(p = .97,
                      mean = 3.34,
                      sd = .07
            ), digits = 2)

## [1] 3.47

#Q9

round(qnorm(p = .91,
            mean = 75.8,
            sd = 8.1
            ), digits = 0) 

## [1] 87

#Q10

##binominal

dbinom(x = 96,
       size = 155,
       prob = .61
       )

## [1] 0.06402352

###normal

n <- 155
pi <- .61

dnorm(x = 96,
      mean = n*pi,
      sd = sqrt(155*.61*.39)
      )

## [1] 0.06385071