Answer to Question #216530 in Statistics and Probability for aasa

Question

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)

Answer 1

a)

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

b)

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

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

c)

$$P(-1.98<Z<0.49)=P(Z<0.49)-P(Z\leq-1.98)$$

$$\approx0.6879331-0.0238518\approx0.664081$$

d)

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

$$\approx0.8887678-0.6984682\approx0.190300$$

e)

$$P(-1.75\leq Z\leq -1.04)=P(Z\leq-1.04)-P(Z<-1.75)$$

$$\approx0.1491700-0.0400592\approx0.109112$$