Is weapon detection at LAX (72 out of 100) consistent with the national rate of 0.80?

X   ~   binomial (n = 100, π)

H0:   π = 0.80        HA:   π < 0.80


A simulation was used earlier to find the approximate p-value for this test by generating repeated samples from a population with π = 0.80. This page illustrates that the binomial distribution can give the p-value directly without simulation.

The p-value is a sum of binomial probabilities

Firstly repeat the simulation — click Accumulate then hold down Simulate until about 100 samples of 100 'weapons' have been generated. This gives an approximation to the p-value.

Now select Binomial distribution from the pop-up menu. The exact probability of getting 72 or fewer weapons detected is 0.0342 if π = 0.80. This is the p-value for the test.

The conclusion is the same as before:

Detecting only 72 weapons would be unlikely if LAX had the same security as elsewhere so there is strong evidence that its detection rate is lower than 0.80.


In 1987, the Federal Aviation Administration (FAA) investigated security at Los Angeles International Airport (LAX). In one test, it was found that only 72 out of 100 mock weapons that FAA inspectors tried to carry onto planes were detected by security guards (Gainesbille Sun, Dec 11, 1987).