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Re: The weights of potatoes grown on a large farm are approximately normal [#permalink]
rahulp11 wrote:
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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Re: The weights of potatoes grown on a large farm are approximately normal [#permalink]
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Dipu10 wrote:
rahulp11 wrote:
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 ?"


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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Re: The weights of potatoes grown on a large farm are approximately normal [#permalink]
Bunuel wrote:
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


Are we required to remember 2.5% falls below 2SD ?
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Re: The weights of potatoes grown on a large farm are approximately normal [#permalink]
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Re: The weights of potatoes grown on a large farm are approximately normal [#permalink]
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