[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″]<\/p>\n
The correct answer is $\\boxed{\\text{B}}$.<\/p>\n
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.<\/p>\n
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 $x=-2$.<\/p>\n
[asy]
\nunitsize(1 cm);<\/p>\n
draw((0,-3)–(0,3));
\ndraw((-3,0)–(3,0));<\/p>\n
real g(real x) {
\n return exp(-(x-1)^2\/4)\/sqrt(2*pi);
\n}<\/p>\n
draw(graph(g,-3,3),red);<\/p>\n
label(“$x$”, (3,0), E);
\nlabel(“$y$”, (0,3), N);
\nlabel(“$f(x)$”, (1.5,0.15), S);
\nlabel(“$P(X<0)$”, (-2,0.15), S);
\n[\/asy]<\/p>\n","protected":false},"excerpt":{"rendered":"
[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″]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[691],"tags":[],"class_list":["post-20291","post","type-post","status-publish","format-standard","hentry","category-probability-and-statistics","no-featured-image-padding"],"yoast_head":"\n