I am working on test prep and have the following problem which I just can't wrap my head around:
A manufacturer knows that, on average, 30% of the widgets it produces require repairs with 1 year after they are sold. Suppose that 10 widgets are randomly selected and let the r.v. X be the number of widgets that require repairs.
Find the number $x$ such that the probability that at least $x$ of them will require repairs is less than 0.5.
I would very much appreciate any insight, because I've been staring at this for 3 hours and I'm drawing a blank.