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Bunuel
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The weights of potatoes grown on a large farm are approximately normal 26 Oct 2021, 03:30
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The weights of potatoes grown on a large farm are approximately normally distributed with a mean of 8.7 ounces and a standard deviation of 1.8 ounces. Approximately 2.5% of the potatoes have a weight below a cutoff value at which they are too small to sell. Which of the following will be closest to this cutoff value?

(A) 3.3 ounces

(B) 4.2 ounces

(C) 5.1 ounces

(D) 6.2 ounces

(E) 6.9 ounces
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The weights of potatoes grown on a large farm are approximately normal 26 Oct 2021, 06:50
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Hello guys!

I'm quoting my answer below:

Since the weight follows the normal distribution the percentage which is closer to 2,5% can be "seen" as the 2,14% of normal distribution, which has a value Xmean-3 s.d = 8,7 - 3*(1,8) = 3,3.

So, my answer choice is "A".
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The weights of potatoes grown on a large farm are approximately normal 22 Dec 2021, 00:07
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The hint is that weight follows a normal distribution and "2.5%" indicates that the potatoes fall beyond 2nd standard deviations from the mean.

Hence we are required to find the value that's 2SD from the mean

8.7oz - 2(1.8) = 5.1oz

Ans: C
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The weights of potatoes grown on a large farm are approximately normal 23 Dec 2021, 03:35
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rahulp11
The hint is that weight follows a normal distribution and "2.5%" indicates that the potatoes fall beyond 2nd standard deviations from the mean.

Hence we are required to find the value that's 2SD from the mean

8.7oz - 2(1.8) = 5.1oz

Ans: C
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Could you please elaborate how "2.5% indicates that the potatoes fall beyond 2nd standard deviations from the mean ?"
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The weights of potatoes grown on a large farm are approximately normal 23 Dec 2021, 04:34
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Dipu10
rahulp11
The hint is that weight follows a normal distribution and "2.5%" indicates that the potatoes fall beyond 2nd standard deviations from the mean.

Hence we are required to find the value that's 2SD from the mean

8.7oz - 2(1.8) = 5.1oz

Ans: C


Could you please elaborate how "2.5% indicates that the potatoes fall beyond 2nd standard deviations from the mean ?"
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Sure. When dealing with normal distribution, certain percentages are associated with Standard Deviations that you just need to remember. These percentages are based on the empirical rule(68-95-99.7 Rule) of normal distribution. The below image is the famous "Bell Curve" which is the graphical representation of normal distribution.




The 68-95-99.7 Rule states that for any normally distributed random variable,
68% of the population will lie within 1 standard deviation, 1SD, of the mean; (which means, 34% on each side)
95% of the population will lie within 2 standard deviations, 2SD, of the mean (which means, 34+13.5% on each side)
99.7% of the population will lie within 3 standard deviations, 3SD, of the mean (which means, 34+13.5%+2.4% on each side)

Hope this helps. For further reading, try the below link.

https://magoosh.com/statistics/understanding-normal-distribution/
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The weights of potatoes grown on a large farm are approximately normal 28 Dec 2021, 08:55
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Bunuel
The weights of potatoes grown on a large farm are approximately normally distributed with a mean of 8.7 ounces and a standard deviation of 1.8 ounces. Approximately 2.5% of the potatoes have a weight below a cutoff value at which they are too small to sell. Which of the following will be closest to this cutoff value?

(A) 3.3 ounces

(B) 4.2 ounces

(C) 5.1 ounces

(D) 6.2 ounces

(E) 6.9 ounces
Show more

Are we required to remember 2.5% falls below 2SD ?
TIA
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The weights of potatoes grown on a large farm are approximately normal 23 Jun 2025, 13:53
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