In: Statistics and Probability
2. Find the value of ? in the following cases:
a. ?(−? ≤ ? ≤ ?) = 0.6840
b. ?(? ≤ ? ≤ 1.40) = .8240
c. ?(−1.20 ≤ ? ≤ ?) = .5860
Solution-A:
use pnormGC in R studio to get the area
Rcode:
library(tigerstats)
pnormGC(bound=c(-1.002712, 1.002712),region="between",mean=0,sd=
1,graph=TRUE)
Output:
pnormGC(bound=c(-1.002712, 1.002712),region="between",mean=0,sd=
1,graph=TRUE)
[1] 0.6840002
P(-1.002712<z<1.002712)=0.684
Solution-b:
pnormGC(bound=c(-1.309,1.40),region="between",mean=0,sd= 1,graph=TRUE)
Output:
P(-1.309<z<1.4)=0.824
c=-1.309
Solution-c:
Rcode:
pnormGC(bound=c(-1.20,0.5276),region="between",mean=0,sd= 1,graph=TRUE)
output:
> pnormGC(bound=c(-1.20,0.5276),region="between",mean=0,sd=
1,graph=TRUE)
[1] 0.5860418
P(-1.20<Z<0.5276)=0.586
c=0.5276