Question

Find the value of the standard normal random variable ?, called ?0 such that:

(a)  ?(?≤?0)=0.6317
?0=

(b)  ?(−?0≤?≤?0)=0.2478
?0=

(c)  ?(−?0≤?≤?0)=0.7208
?0=

(d)  ?(?≥?0)=0.2224
?0=

(e)  ?(−?0≤?≤0)=0.3974
?0=

(f)  ?(−1.83≤?≤?0)=0.8711
?0=

Answer 1

(a)  ?(?≤?0)=0.6317
?0= 0.34

(by using z-table)

(b)  ?(−?0≤?≤?0)=0.2478

?(z<−?0) = (1 - 0.2478)/2

?(z<−?0) = 0.3761
-?0= -0.32

?0= 0.32

(by using z-table)

(c)  ?(−?0≤?≤?0)=0.7208

?(z<−?0) = (1 - 0.7208)/2 = 0.1396
-?0= -1.08

(by using z-table)

?0= 1.08

(d)  ?(?≥?0)=0.2224

?(?<?0) =1 - 0.2224= 0.7776

?0= 0.76

(by using z-table)

(e)  ?(−?0≤?≤0)=0.3974

?(z<−?0) = (0.5 - 0.3974) = 0.1026
-?0= -1.27

(by using z-table)

?0= 1.27

(f)  ?(−1.83≤?≤?0)=0.8711

?(−1.83≤?≤?0)= ?(?≤?0) - ?(?≤-1.83)

?(−1.83≤?≤?0)= ?(?≤?0) - 0.0336

0.8711= ?(?≤?0) - 0.0336

?(?≤?0) = 0.8711 + 0.0336

?(?≤?0) = 0.9047

?0= 1.31