Question

2. Area under the normal curve a. Area between 2 sd above and the mean (z scores of 0 and 2.0) b. Area below z score of 1 c. Z score below which 95% of all values fall

Answer 1

Solution2a:

P(0<X<2) to be found.

use pnormGC function in R.std normal distributions are with mean=0 and sd=1

Use R software

Rcode:

library(tigerstats)
pnormGC(c(0,2),region="between",mean=0,sd=1,graph=TRUE)

0.4772

Solutionb:

P(Z<1) to be found

pnormGC(bound=1,region="below", mean=0,sd=1,graph=TRUE)

0.8413

That is P(Z<1)=0.8413

Solutionc:

For z score -2 and 2

95% of teh area lies

Rcode is

pnormGC(c(-2,2),region="between",mean=0,sd=1,graph=TRUE)

P(-2<Z<2)=0.9545

=0.9545*100

=95.45%