Answer to Question #216530 in Statistics and Probability for aasa

Question #216530

Given that z is a standard normal random variable, compute the following

probabilities.

a) P (Z < 0.49)

b) P (0.52 < Z)

c) P (- 1.98 ≤ Z ≤ .49)

d) P (.52 ≤ Z ≤ 1.22)

e) P (- 1.75 ≤ Z ≤ - 1.04)


1
Expert's answer
2021-07-14T09:31:26-0400

a)

P(Z<0.49)=0.687933P(Z<0.49)=0.687933

b)

P(Z>0.52)=0.301532P(Z>0.52)=0.301532


P(Z<0.52)=0.698468P(Z<0.52)=0.698468

c)


P(1.98<Z<0.49)=P(Z<0.49)P(Z1.98)P(-1.98<Z<0.49)=P(Z<0.49)-P(Z\leq-1.98)

0.68793310.02385180.664081\approx0.6879331-0.0238518\approx0.664081

d)


P(0.52Z1.22)=P(Z1.22)P(Z<0.52)P(0.52\leq Z\leq 1.22)=P(Z\leq1.22)-P(Z<0.52)

0.88876780.69846820.190300\approx0.8887678-0.6984682\approx0.190300

e)


P(1.75Z1.04)=P(Z1.04)P(Z<1.75)P(-1.75\leq Z\leq -1.04)=P(Z\leq-1.04)-P(Z<-1.75)

0.14917000.04005920.109112\approx0.1491700-0.0400592\approx0.109112


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