Suppose someone receives 12 texts per hour.

What is the probability that this person received more than 4 texts in 10 minutes?

I'm clueless about how to start this. I know i have to use random variables and possibly cdf, but not how.

  • 1
    $\begingroup$ To solve this problem, we would need to know the probability distribution of text receiving. I'm guessing it's Poisson with $\lambda=12$. $\endgroup$ – John Jun 25 '18 at 0:59
  • $\begingroup$ The problem doesn't mention the distribution. I guess that's why i'm clueless $\endgroup$ – Peplm Jun 25 '18 at 1:04

$X\sim Po(\frac{12}{6})=X\sim Po(2)$
P$(X>4) =$ $1-$P$(X\leq4)=1-0.9473=0.0527$

  • $\begingroup$ Thanks. But what justifies the poisson dist? $\endgroup$ – Peplm Jun 25 '18 at 1:51
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    $\begingroup$ Without context, just a guess based on similar probability problems.(+1) In context, it would be a good bet you've studied Poisson distributions recently. Notice the importance of adapting the Poisson rate to the specific question asked. Rate is 12/hr (on average!), but question is about 10 min, and rate is 2 per 10 min. $\endgroup$ – BruceET Jun 25 '18 at 1:57
  • $\begingroup$ thanks for answering his question. $\endgroup$ – Chris2018 Jun 25 '18 at 1:59

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