Furniture manufacturing companies often deal with the quality of the drilling of dowel holes. Consider the case of

Company $x,$ which believes that when the drilling process is operating at an acceptable rate, the upper limit on the

percentage of incorrectly drilled dowel holes is $8\%.$ To monitor its drilling process, the company randomly samples $10$

products each hour and determines if the dowel hole in each product is correctly drilled or not. If$,$ in the sample of $10$

holes, $1$ or more incorrectly drilled holes is discovered, the production process is stopped and the drilling process is

recalibrated. Use this information to complete parts a through c$.$

a$.$ If the process is really operating correctly $(p=0\mathrm{.}08),$ what is the probability that the sampling effort will produce

$x=0$ defective holes and thus the process will properly be left to continue running?

$($Round to four decimal places as needed.$)$