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Mangoes that are marketed by a particular orchard have masses which are normally distributed with mean mass $20.5g$ and standard deviation $4g$. The mangoes are packed into packets of $10$ mangoes per packet.

What is the probability that $4$ consecutive packets of the $5$ packets chosen at random have exactly $6$ mangoes with masses greater than $20.1g$ ?

My attempt

I found that the probability that its mass is greater than $20.1g$ is $0.5938$, the probability that exactly $6$ mangoes from $10$ that are put into per packet have masses that are greater than $20.1g$ is $0.233$, now I don't know how to find the answer of $4$ consecutive packets of the $5$ packets chosen at random have exactly $6$ mangoes with masses greater than $20.1$

callculus42
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Heng Yong Wei
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  • What is YOUR question ? – callculus42 Nov 16 '16 at 09:19
  • I found that the probability that its mass is greater than 20.1g is 0.5938, the probability that exactly 6 mangoes from 10 that are put into per packet have masses that are greater than 20.1g is 0.233, now I don't know how to find the answer of 4 consecutive packets of the 5 packets chosen at random have exactly 6 mangoes with masses greater than 20.1g – Heng Yong Wei Nov 16 '16 at 10:55

1 Answers1

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I have the same results. Only at $0.5938$ you have mixed up the numbers $3$ and $9$. . But it is only a typo, because the probability that exactly $6$ mangoes from $10$ that are put into one packet have masses that are greater than 20.1g is indeed $0.233$

Let one packet with $6$ mangos with masses greater than $21g$ denoted as $g$. And a packet with $6$ mangos with masses smaller than $21g$ is denoted as $s$.

Then you have the following two combinations for $4$ consecutive packets of the $5$ packets chosen at random have exactly $6$ mangoes with masses greater than $20.1$:

$ggggs$ and $sgggg$

The probability for one combination is $(0.233)^4\cdot (1-0.233)$

And for two combinations it is twice as much. This is the asked probability.

callculus42
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