Embedding extra styles with noscript

<head>
...
 <script type="text/javascript">
 //<![CDATA[
  document.write('<style type="text/css">.noscript{display:none}</style>');
 //]]>
 </script>
...
</head>

<!doctype html><html>
<head><noscript><style>body{background:red}</style></noscript></head>
<body>is this red? it should <script>document.writeln("not");</script> be. <noscript>indeed.</noscript></body>
</html>