Question

7.

a.

b.

Assume that random guesses are made for nine multiple choice questions on an SAT test, so that there are n = 9 trials, each with probability of success (correct) given by p = 0.2. Find the indicated probability for the number of correct answers. Find the probability that the number x of correct answers is fewer than 4. P(X<4)= (Round to four decimal places as needed.)

c.

Answer 1

Solution-a:

Binomial distribution

X~B(9,0.2)

Use pbinomGC in R studio to get the answer:

library(tigerstats)
pbinomGC(bound=3,region="below", size=9,prob=0.2,graph=TRUE)
0.9143583

ANSWER:

P(X<3)=0.9144

Solution-b:

n=2 p=0.5

P(no correct answers)=P(X=0)

pbinomGC(bound=c(0,0),region="between", size=2,prob=0.5,graph=TRUE)

binom(2,0.5) Distribution: Shaded Area 0.25 0 X (X)d 0 00 0.2 0.3 0.4 0.5

=0.25

ANSWER:

P(no correct answers)=0.250

Solution-c:

n=8

x=6

p=0.46

Rcode:

library(tigerstats)
pbinomGC(bound=c(6,6),region="between", size=8,prob=0.46,graph=TRUE)

0.07735574

binom(8,0.46) Distribution: Shaded Area= 0.077 X (x)d 00 0 0.10 0.20

the probability is 0.0774

Rsceenshot:

RStudio ile Edit Code View Plots Session Build Debug Profile Tools Help Project Addins Go to file/function Untitled8* X Untitled7* x Chapter 4 DSUR Graphs.R*X Chapter 6 DSUR Correlations.R* X Console Untitled3* Chapter 10 DSUR GLM1.R* Terminal Run Source on Save Source library(tigerstats) pbinotGc ( brttund-3,region="below", size=9,prob-0.2,graph=TRUE) pbinotGc ( brttund-c(0,0),region="between", pbinoto gc (bround=c(6,6),region="between", 1 1ibrary(tigerstats) > pbinomGC (bound-3,region="below", size-9,prob-0.2,graph=TRUE) [1] 0.9143583 pbinomGC (bound=c(0,0), region="between", size-2,prob-0.5,graph=TRUE) [1] 0.25 pbinomGC (bound-c (6,6),region="between", [1] 0.07735574 2 3 size=2,prob0.5,graph=TRUE) size=8,prob-0.46,graph=TRUE) 4 size-8,prob-0.46,graph=TRUE)