Due to Covid-19 pandemic, the demand for disposable medical face mask has increased drastically. A particular brand of medical face mask making machine is used to produce disposable medical face masks in mass production. This machine is capable of producing 80 to 100 industry standard surgical style face masks every minute. This particular machine has a 2% defective rate. The production of medical face masks on this machine is considered a random process where each produced mask is independent of the others. Using this information calculate the following probabilities: a) What is the probability that the 10th medical face mask produced is the first with a defeci. b) What is the probability that the face mask making machine produces no defective mask in a batch of 100? ( ) c) On average, how many face masks would you expect to be produced before the first defective mask? What is the standard deviation? (. d) Another brand of this machine that also produces surgical style face masks has a 5% defective rate where each mask is produced independently of the others. On average how many face masks would you expect to be produced with this machine before the first with a defect? What is the standard deviation? e) Based on your answers to parts (c) and (d), how does increasing the probability of an event (defect in this case) affect the mean and standard deviation of the wait time until the event's occurrence (defect in this case)?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Transcribed Image Text:Due to Covid-19 pandemic, the demand for disposable medical face mask has increased drastically. A particular brand of medical face mask making machine is used to produce disposable medical face masks in mass production. This machine is capable of producing 80 to 100 industry standard surgical style face masks every minute. This particular machine has a 2% defective rate. The production of medical face masks on this machine is considered a random process where each produced mask is independent of the others. Using this information calculate the following probabilities: a) What is the probability that the 10th medical face mask produced is the first with a defeci. b) What is the probability that the face mask making machine produces no defective mask in a batch of 100? ( ) c) On average, how many face masks would you expect to be produced before the first defective mask? What is the standard deviation? (. d) Another brand of this machine that also produces surgical style face masks has a 5% defective rate where each mask is produced independently of the others. On average how many face masks would you expect to be produced with this machine before the first with a defect? What is the standard deviation? e) Based on your answers to parts (c) and (d), how does increasing the probability of an event (defect in this case) affect the mean and standard deviation of the wait time until the event's occurrence (defect in this case)?

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