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The figure above shows a normal distribution with mean m and

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The figure above shows a normal distribution with mean m and [#permalink] New post 31 May 2019, 09:54
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#GREexcercise The figure above shows a normal distribution.jpg
#GREexcercise The figure above shows a normal distribution.jpg [ 21.44 KiB | Viewed 240 times ]


The figure above shows a normal distribution with mean m and standard deviation d, including approximate percents of the distribution corresponding to the six regions shown.

Suppose the heights of a population of 3,000 adult penguins are approximately normally distributed with a mean of 65 centimeters and a standard deviation of 5 centimeters.

(a) Approximately how many of the adult penguins are between 65 centimeters and 75 centimeters tall?
(b) If an adult penguin is chosen at random from the population, approximately what is the probability that the penguin’s height will be less than 60 centimeters? Give your answer to the nearest 0.05.

[Reveal] Spoiler: OA
(a) 1,440 (b) 0.15



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Re: The figure above shows a normal distribution with mean m and [#permalink] New post 02 Jun 2019, 09:52
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Carcass wrote:
Attachment:
#GREexcercise The figure above shows a normal distribution.jpg


The figure above shows a normal distribution with mean m and standard deviation d, including approximate percents of the distribution corresponding to the six regions shown.

Suppose the heights of a population of 3,000 adult penguins are approximately normally distributed with a mean of 65 centimeters and a standard deviation of 5 centimeters.

(a) Approximately how many of the adult penguins are between 65 centimeters and 75 centimeters tall?
(b) If an adult penguin is chosen at random from the population, approximately what is the probability that the penguin’s height will be less than 60 centimeters? Give your answer to the nearest 0.05.

[Reveal] Spoiler: OA
(a) 1,440 (b) 0.15


Image


GIVEN: The heights are approximately normally distributed with a mean of 65 centimeters and a standard deviation of 5 centimeters.
Let's add this information to the diagram to get:
Image


(a) Approximately how many of the adult penguins are between 65 centimeters and 75 centimeters tall?
From the diagram...
Image
...we can see that 48% of the heights are between 65 centimeters and 75 centimeters.
So, the NUMBER of the penguins between 65 cm and 75 cm = 48% of 3000 = 1440

Answer: 1440
----------------------------------------------------------
(b) If an adult penguin is chosen at random from the population, approximately what is the probability that the penguin’s height will be less than 60 centimeters? Give your answer to the nearest 0.05
From the diagram...
Image
...we can see that 16% of the heights are less than 60 centimeters.
So, P(chosen penguin is less than 60 cm tall) = 16% = 0.16

IMPORTANT: the question asks for the answer to be to the nearest 0.05
So, possible answers are: 0.05, 0.10, 0.15, 0.20, 0.25, 0.30,...etc
So, 0.15 is the closest to 0.16

Answer: 0.15

Cheers,
Brent
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Re: The figure above shows a normal distribution with mean m and   [#permalink] 02 Jun 2019, 09:52
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