In the 1990s, most product package designs were retained for 7 years or more. But now packages are redesigned, on average, once every 2 years. [Source: L. Story, "Product packages now shout to grab your fickle attention," The New York Times, August 10, 2007.] You randomly select a package and track it for the next 5 years. What's the probability that it will be redesigned exactly three times?

Question

Jacqueline Tyler

Mathematics

9 July, 23:02

In the 1990s, most product package designs were retained for 7 years or more. But now packages are redesigned, on average, once every 2 years. [Source: L. Story, "Product packages now shout to grab your fickle attention," The New York Times, August 10, 2007.] You randomly select a package and track it for the next 5 years. What's the probability that it will be redesigned exactly three times?

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Briana Blanchard · Answer 1

The probability that a package will be redesigned exactly three times in the next 5 years = 0.21376

Step-by-step explanation:

This problem can be modelled as a Poisson distribution problem.

Poisson distribution formula is given as

P (X = x) = (e^-λ) (λˣ) / x!

where λ = mean = average number of times a package gets redesigned = 1 time per 2 years = 2.5 times per 5 years.

x = variable whose probability is required = exactly 3 times in 5 years.

P (X = 3) = (e⁻²•⁵) (2.5³) / 3!

P (X=3) = 0.21376