Due to recent finding for cracks on glass vials at the end of the line inspection, Hy-Tech Healthcare; engineer randomly selects 100 vials from the 6 active production lines producing glass vials. Engineer observes 14 vials defective vial out of 100. He suspects that 14 or more defects occurring in production line 5 based on preventive maintenance report. Calculate the probability and conclude if the engineer suspicion was right about production line 5

6.3 The waiting time If until the rst error in a binary sequence is described by the (type 1} geometric PDF. Let the probability of an error be p = US. [a] Compute the mean and Variance of K. (b) Apply the Markov inequality to bound the probability of the event K 23 16. [e]: Use the Cbebyshev inequality to bound the probability of this event. (cl) Use the oue~sidetl {Zlhebyshetr inequality to bound the probability. {e} Compute the actual probability of the event K E 16. {Child} la=3 Problem 3: Consider a normal random variable X with mean p and standard deviation o. a) Prove the Chebyshev inequality b) Assume u = -1 and o = 1. Evaluate the following probabilities: P(X