Inspection of a random sample of 40 aircraft showed that 27 needed repairs to fix a wiring problem that might compromise safety.
(a) How large a sample would be needed to estimate the true proportion of jets with the wiring problem, with 90 percent confidence and an error of ± 6 percent? (Enter your answer as a whole number (no decimals). Use a z-value taken to 3 decimal places in your calculations.)
(b) Would the airline actually conduct further sampling, or just inspect all the planes?