[amp_mcq option1=”0.5″ option2=”greater than zero and less than 0.5″ option3=”greater than 0.5 and less than 1.0″ option4=”1″ correct=”option1″]
The correct answer is $\boxed{\text{B}}$.
A normal random variable with mean 1 and variance 4 has a standard deviation of 2. The probability that a normal random variable is less than 0 is equal to the area under the curve to the left of $x=-2$. This area is less than 0.5 but greater than 0.
The following figure shows the probability density function of a normal random variable with mean 1 and variance 4. The shaded area is the area under the curve to the left of $x=-2$.
[asy]
unitsize(1 cm);
draw((0,-3)–(0,3));
draw((-3,0)–(3,0));
real g(real x) {
return exp(-(x-1)^2/4)/sqrt(2*pi);
}
draw(graph(g,-3,3),red);
label(“$x$”, (3,0), E);
label(“$y$”, (0,3), N);
label(“$f(x)$”, (1.5,0.15), S);
label(“$P(X<0)$”, (-2,0.15), S);
[/asy]