Question

6. Find the value of ? for each of the following probability statements, and sketch the corresponding area. (4 pts each)

a. P (-1.0 < Z < ?) = .6898

b. P (1.0 < Z < ?) = .0072

c. P(-2.0 < Z < ?) = .9544

d. P(-2.0 < Z < ?) = .0164

Answer 1

Solution(a)

P(-1.0<Z<?) = 0.6898

P(Z<z) - P(Z<-1.0) = 0.6898

P(Z<z) = 0.6898 + 0.1587 = 0.8485

Z = 1.03

P(-1.0<Z<1.03) = 0.6898

Solution(b)

P(1.0<Z<?) = 0.0072

P(Z<z) = 0.0082 + P(Z<1) = 0.0072 + 0.8413 = 0.8485

z = 1.03

P(1.0<Z<1.03 ) = 0.0072

Solution(c)

P(-2.0<Z<0) = 0.9544

P(Z<z) = 0.9544 + P(Z<-2.0) = 0.9544 + 0.0228 = 0.9772

Z = 2

P(-2.0<Z<2.0) = 0.9544

Solution(d)

P(-2.0<Z<?) = 0.0164

P(Z<z) = 0.0164 + 0.0228 = 0.0392

P(-2.0<Z<-1.76) = 0.0164