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(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

Respuesta :

Answer:

Step-by-step 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

=[tex]P(-2.16<z<-0.65)\\=0.4846-0.2422\\=0.2424[/tex]

c) [tex](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[/tex]

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