Question

Find the area under the standard normal curve between:

(a) P(-1.5<z<1.25)

(b) to the right of z=1.06

P(z<-2.58 or z>2.58)

Answer 1

Note: Z~N(0,1)

So, P(Z<z) or P(Z<=z) is th cdf of standard normal, it can be derived from R studio : code : pnorm(z) or standard normal table

a) P(-1.5< z< 1.25) = P(Z<1.25) - P(Z<-1.5) = 0.8943502 - 0.0668072 = 0.827543

b) P(Z>1.06) = 1-P(Z<=1.06) =1- 0.8554277 = 0.1445723

c) P(Z<-2.58 or Z>2.58) = P(Z<-2.58) +P( Z>2.58) = P(Z<-2.58) +1-P( Z<2.58) = 0.00494 +(1- 0.9956) = 0.00988

R Codes:

> pnorm(1.25)
[1] 0.8943502

pnorm(-1.5)
[1] 0.0668072
> pnorm(1.06)
[1] 0.8554277
> pnorm(-2.58)
[1] 0.004940016
> pnorm(2.58)
[1] 0.99506