The sensitivity of a walkthrough security detector at an air

The sensitivity of a walk-through security detector at an airport is set so that, on average, 0.1% of the people who pass through the detector set off an alarm and requires searching (in other words p=0.001). If 8000 people walk through the security detector

a. What is the probability that fewer than 7 people will set off the alarm?

b. What is the probability that more than 6 people will set off the alarm?

Please explain your answers step by step

Solution

X no of people set of an alarm is Binomial with p = 0.001 and n =8000

a) probability that fewer than 7 people will set off the alarm = P(X<7) =

= P(X=0 or 1 or 2...or 6) = sum of 1000Cr(0.001)^r(0.999)^1000-r, r= 0,1,2,3,4,5,6

0.9999

b) probability that more than 6 people will set off the alarm = P(X>6)

8.197x10^-5