Answer to Question #113707 in Statistics and Probability for Katenda

Question

Question 15

Given that P(-2 ≤ Z ≤ z) = 0.4019, what is the value of z?

(1) 0.19
(2) 0.19
(3) 0.4247
(4) 0.5753
(5) None of the above

Answer 1

$P(-2\le Z\le z)=0.4019\\$

then,

$P(-2\le Z\le0)=0.4772$

since $P(-2\le Z\le0)\ge P(-2\le Z\le z)$ , z is negative value.

Therefore,

$P(-2\le Z\le0)-P(z\le Z\le0)=0.4019\\ 0.4772-P(z\le Z\le0)=0.4019\\ P(z\le Z\le0)=0.0753\\$

that means,

$P(z\ge Z)=0.5-0.0753=0.4247\\ \bold{z=-0.19}$

among those five answers there isn't -0.19 therefore the answer is $5^{th}$ one.

(5) none of the above