What is the probability that out of 40 trials of your new ma

What is the probability that, out of 40 trials of your new magnetically-coupled actuator, you find more than 3 failures, if on an average magnetically-coupled actuators fail 5% of the time.

Solution

let X be the random variable denoting the number of failures out of 40 trials of magnetically coupled actuator.

on average magnetically coupled actuator fail 5% of the time.

so the probability of failure is 0.05

so X~Bin(40,0.05)

here the required probability is

P[X>3]=1-P[X<=3]=1-0.861850=0.13815 [answer]