The FAA Wildlife Strike Database contains records of reporte

The FAA Wildlife Strike Database contains records of reported wildlife strikes since 1990. Strike reporting is voluntary. Therefore, this database only represents the information received from airlines, airports, pilots, and other sources. The full dataset, consisting of 145,000 reported incidents in order of occurrence with 94 variables recorded for each, was downloaded from the FAA on 21-Jan-2014. Suppose that the airspeed at which wildlife strikes is normally distributed with a mean of 141 knots and a standard deviation of 47 knots. What is the probability (correct to three decimal places) that the mean airspeed of 10 randomly selected wildlife strikes is at most 100 knots?

Solution

So the probability (correct to three decimal places) that the mean airspeed of 10 randomly selected wildlife strikes is at most 100 knots is

P(xbar>100) = P((xbar-mean)/(s/vn) >(100-141)/(47/sqrt(10)))

=P(Z>-2.76) =0.9971 (from standard normal table)