5. At Express Delivery Service, providing high-quality service to its customers

Question

5. At Express Delivery Service, providing high-quality service to its customers is the top priority of management. The company guarantees a refund of charges if a package it is delivering does not arrive to its destination on time. Despite all efforts, 94% of the packages mailed through the company arrive at their destinations on time. A Corporation mailed seven packages through Express Delivery on Monday. a) Find the probability that all of the seven packages will arrive on time. b) Find the probability that exactly two of these seven packages will not arrive on time. c Interpret the meaning of your answer to part b.

Explanation / Answer

Binomial distribution parameters

n = 7, p = 0.94, q = 0.06

Probability mass function, p[x] = ncx px qn-x, x = 0,1,2.....7

a) p [x = 7] = pn

= 0.947

= 0.6485

b) p[2 of the packages will not arrive] = 1 - p[x =2]

= 1 - 7c2 * 0.942 * 0.065

= 1 - 0.0000144

= 0.99998

c) Given event is part b is almost sure event

since it probability is exactly close to '1'

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