A certain snack vending machine dispenses the incorrect item, on average, 4.2 times every day. Assume that the number of incorrect items dispensed on any given day, X, is a Poisson random variable.  What is the probability that the machine will dispense exactly 9 incorrect items tomorrow? ANSWER:  (Use only the appropriate formula and/or statistical table in your textbook to answer this question. Report your answer as to 4 decimal places, using conventional rounding rules)  What is the standard deviation of this probability distribution? ANSWER:  (Use only the appropriate formula and/or statistical table in your textbook to answer this question. Report your answer as to 4 decimal places, using conventional rounding rules)

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Asked Nov 1, 2019
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A certain snack vending machine dispenses the incorrect item, on average, 4.2 times every day. Assume that the number of incorrect items dispensed on any given day, X, is a Poisson random variable.

 

 

What is the probability that the machine will dispense exactly 9 incorrect items tomorrow? ANSWER:  (Use only the appropriate formula and/or statistical table in your textbook to answer this question. Report your answer as to 4 decimal places, using conventional rounding rules)

 

 

What is the standard deviation of this probability distribution? ANSWER:  (Use only the appropriate formula and/or statistical table in your textbook to answer this question. Report your answer as to 4 decimal places, using conventional rounding rules)

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Expert Answer

Step 1

The snack vending machine dispenses the incorrect item on average 4.2 times per day.

Thus,

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= 4.2 x Poisson(4.2) -42 (4.2) P(X x) x!

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Step 2

a)

The probability that the machine will dispense exactly 9...

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e(4.2) P(X 9) 9! 0.0168

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