Question

(a) Given a standard normal distribution, find the area under the curve whichlies(i) to the left ofz= 1.43;(ii) to the right ofz=−0.89;(iii) betweenz=−2.16 andz=−0.65.(b) Given a standard normal distribution, find the value ofksuch that(i)P(Z < k) = 0.0427(ii)P(Z > k) = 0.2946(iii)P(−0.93< Z < k) = 0.7235

Answer 1

Explanation:

Given a standard normal distribution, we can use table to find the probability.

We know that symmetrical about y axis.

a) left of z=1.43 is

b)betweenz=−2.16 andz=−0.65

=
`P(-2.16<z<-0.65)\\=0.4846-0.2422\\=0.2424`

c)
`(i)P(Z < k) = 0.0427\\k=-1.72(ii)P(Z > k) = 0.2946\\k=0.54(iii)P(−0.93< Z < k) = 0.7235\\0.7235=0.3238+c\\c= 0.3997\\k=1.28`