Question

R PROGRAMMING by using R studio or R software

1. The probability that a patient recovers from a rare blood disease is 0.4. If 15 people are known to have contracted this disease, what is the probability that a) at least 10 people survive, b) 3 to 8 people survive, c) exactly 5 people survive? d) Plot the graph of the distribution.

Answer 1

Let x = Number of people survive

X ~ Binomial (n,p)

since n is fixed and p is constant for each trial

R codes marked in BOLD

# (a) probability at least 10 people survive
a <- pbinom(9, 15, 0.4, lower.tail = FALSE)
print(a)

Ans : 0.0338333

# (b)3 to 8 people survive
b <- pbinom(8, 15, 0.4, lower.tail = TRUE)-
pbinom(2, 15, 0.4, lower.tail = TRUE)
print(b)

Ans 0.8778386

# (c) exactly 5 people survive
c <- dbinom(5, 15, 0.4)
print(c)

Ans : 0.1859378

#(d) plot of the distribution
x <- seq(0,15,by=1)
px <- dbinom(x, 15, 0.4)
plot(x,px,main = "Graph of the distribution ",xlab = "x",ylab = "P(X=x)","l")

P(X=x) 0.00 0.05 0.10 0.15 0.20 Graph of the distribution F은

Studio Eile Edit Code View - OR Plots Session Build Debug Profile Lools Help H A Go to file/function - Addins - R Project (None) Run + Source - ® 93.R* * a H Source on Save . 2 # (a) probability at least 10 people survive 3 a <- pbinom(9, 15, 0.4, lower.tail = FALSE) 4 print(a) Environment History Connections Import Dataset - List - C. Global Environment - values 0.0338333028843521 0.877838591066112 0.185937844764672 num (1:16] 0.00047 0.0047 0.0... num (1:16) 0 1 2 3 4 5 6 7 8 ... 6 # (b)3 to 8 people survive b <- pbinom(8, 15, 0.4, lower.tail = TRUE) - pbinom (2, 15, 0.4, lower.tail = TRUE) print(b) 10 13 11 # (c) exactly 5 people survive 12 C <- dbinom (5, 15, 0.4) print(c) 14 15 #(d) plot of the distribution 16 X <- seq(0,15, by=1) 17 px <- dbinom (X, 15, 0.4) 18 plot(x, px, main = "Graph of the distribution ",xlab = "x",ylab = "P(X=x)","1") Files Plots Viewer Packages Zoom Help Export- 15:1 (Top Level) : R Script Graph of the distribution Console Terminal Jobs P(X=x) 0.00 > plot(x,px, main = "Graph of the distribution ",xlab = "x",ylab = "P(x=x)","7") > print (a) [1] 0.0338333 > print (b) [1] 0.8778386 >print(c) [1] 0.1859378 5 10 15 1025 PM 1 Type here to search OEHP e BⓇW Desktop 25-Feb-20