Display number of posts excluding specific category

I’m using a plugin to count the total number of published posts using the following:

$numposts = $wpdb->get_var(“SELECT COUNT(*) FROM $wpdb->posts WHERE post_status = ‘publish’ AND post_type = ‘post'”);
if (0 < $numposts) $numposts = number_format($numposts);
echo $numposts;

I’d like to exclude a specific category so it won’t be counted. I tried adding:

AND post_category != ‘3’

But that did not work. Am I using the wrong thing or does it need to written completely different?

Thanks.