Let Z be a standard normal random variable and calculate the following probabili

Question

Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wherever appropriate. (Round your answer to four decimal places.) (a) P (0 lessthanorequalto Z lessthanorequalto 2.13) (b) P (0 lessthanorequalto Z lessthanorequalto 1) (C) P (-2.20 lessthanorequalto Z lessthanorequalto 0) (d) P (-2.20 lessthanorequalto Z lessthanorequalto 2.20) (e) P (Z lessthanorequalto 1.30) (f) P (-1.55 lessthanorequalto Z) (g) P (-1.20 lessthanorequalto Z lessthanorequalto 2.00) (h) P (1.39 lessthanorequalto Z lessthanorequalto 2.50) (i) P (1.20 lessthanorequalto Z) (j) P ([Z] lessthanorequalto 2.50) You may need to use the appropriate table in the Appendix of Table to answer this question.)

Explanation / Answer

Ans:

a)P(0<=z<=2.13)=P(z<=2.13)-P(z<=0)=0.9834-0.5=0.4834

b)P(0<=z<=1)=P(z<=1)-P(z<=0)=0.8413-0.5=0.3413

c)P(-2.2<=z<=0)=P(z<=0)-P(z<=-2.2)=0.5-0.0139=0.4861

d)P(-2.2<=z<=2.2)=P(z<=2.2)-P(z<=-2.2)=0.9861-0.0139=0.9722

e)P(z<=1.39)=0.9177

f)P(z>=-1.55)=P(z<=1.55)=0.9394

g)P(-1.2<=z<=2)=P(z<=2)-P(z<=-1.2)=0.97725-0.11507=0.8622

h)P(1.39<=z<=2.5)=P(z<=2.5)-P(z<=1.39)=0.9938-0.9177=0.0761

i)P(z>=1.2)=1-P(z<=1.2)=1-0.8849=0.1151

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