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  3. 4. if z is a standard normal random variable, that

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

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Statistics

4. If Z is a standard normal random variable, that is Z ∼ 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(−b < Z < b) = 0.95

Answer & Explanation Solved by verified expert
4.1 Ratings (472 Votes)

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

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

answer: 0.674

c)P(Z > d) = 0.83

P(Z≤d) = 1-0.83 = 0.17

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

answer: -0.954

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

so, value of b = 1.96
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