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 40% of wildlife strikes occur during the day. What is the probability (correct to three decimal places) that in a random sample of 150 wildlife strikes from the original dataset at least 50% occurred during the day?

Solution

So the probability is

P(phat>=0.5) = P((phat-p)/sqrt(p*(1-p)/n) >(0.5-0.4)/sqrt(0.4*0.6/150))

=P(Z>2.5)

=0.0062 (from standard normal table)