Question

In: Statistics and Probability

2. Find the value of ? in the following cases: a. ?(−? ≤ ? ≤ ?)...

2. Find the value of ? in the following cases:

a. ?(−? ≤ ? ≤ ?) = 0.6840

b. ?(? ≤ ? ≤ 1.40) = .8240

c. ?(−1.20 ≤ ? ≤ ?) = .5860

Solutions

Expert Solution

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


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