4 If Z is a standard normal random variable, that is Z N(0,1), (a) w...

a PZ 1000 08413 answer bZ value at 075 0674 excel formula NORMSINV 075 an ....

4. If Z is a standard normal random variable, that is Z âˆ¼ N(0, 1), (a)...

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4. If Z is a standard normal random variable, that is Z âˆ¼ N(0,1), (a) what is P(Z 2 < 1)? (b) Find a number c such that P(Z< c) = 0.75 (c) Find a number d such that P(Z > d) = 0.83 (d)Find a number b such that P(âˆ’b < Z < b) = 0.95

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4.1 Ratings (472 Votes)

a) P(Z < 1.000Â Â ) =Â Â 0.8413 (answer)

b)Z value at Â Â 0.75Â Â =Â Â 0.674Â Â (excel formula =NORMSINV(Â Â 0.75Â Â ) )

answer: 0.674

c)P(Z > d) = 0.83

P(Zâ‰¤d) = 1-0.83 = 0.17

Z value at Â Â 0.17Â Â =Â Â -0.954Â Â (excel formula =NORMSINV(Â Â 0.17Â Â ) )

answer: -0.954

d)proportion=Â Â 0.9500Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â
proportion left Â Â 0.0500Â Â is equally distributed both left and right side of normal curveÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â
z value atÂ Â 0.025Â Â = Â±Â Â 1.960Â Â (excel formula =NORMSINV(Â Â 0.05Â Â / 2 ) )Â Â

so, value of b = 1.96

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