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The lengths of a certain population of earthworms are normal
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28 Jul 2018, 16:30
28 Jul 2018, 16:30
Expert Reply
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Question Stats:
80% (00:55) correct
19% (00:35) wrong based on 46 sessions
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The lengths of a certain population of earthworms are normally distributed with a mean length of 30 centimeters and a standard deviation of 3 centimeters. One of the worms is picked at random.
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
The probability that the worm is between 24 and 30 centimeters, inclusive |
The probability that the worm is between 27 and 33 centimeters, inclusive |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Re: The lengths of a certain population of earthworms are normal
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04 Aug 2018, 19:16
04 Aug 2018, 19:16
Mean = 30
SD = 3
Hence 1 SD below the mean = 27
and 2 SD below the mean = 24
Therefore for normal distribution the% of date at the given range will be 13.5 + 34 = 47.5
While for qtyB the % of data at the given range will be 1 SD above and 1 SD below the mean = 68
Posted from my mobile device
SD = 3
Hence 1 SD below the mean = 27
and 2 SD below the mean = 24
Therefore for normal distribution the% of date at the given range will be 13.5 + 34 = 47.5
While for qtyB the % of data at the given range will be 1 SD above and 1 SD below the mean = 68
Posted from my mobile device
Re: The lengths of a certain population of earthworms are normal
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12 Aug 2018, 16:22
12 Aug 2018, 16:22
1
Expert Reply
Explanation
Normal distributions are always centered on and symmetrical around the mean, so the chance that the worm’s length will be within a certain 6-centimeter range (or any specific range) is highest when that range is centered on the mean, which in this case is 30 centimeters.
More specifically, Quantity A equals the area between –2 standard deviations and the mean of the distribution. In a normal distribution, roughly 34 + 34 + 14 + 14 = 96% of the sample will fall within 2 standard deviations above or below the mean. Limit yourself only to the 2 standard deviations below the mean, then half of that, or 96%÷2 = 48%, falls in this range. In contrast, Quantity B equals the area between –1 standard deviation and +1 standard deviation. In a normal distribution, roughly 34 + 34 = 68% of the sample falls within 1 standard deviation above or below the mean. Since 68% is greater than 48%, Quantity B is greater.
Note that exact figures are not required to answer this question! Picture any bell curve—the area under the “hump” (that is, centered around the middle) is bigger! Thus, it has more members of the dataset (in this case, worms) in it.
Normal distributions are always centered on and symmetrical around the mean, so the chance that the worm’s length will be within a certain 6-centimeter range (or any specific range) is highest when that range is centered on the mean, which in this case is 30 centimeters.
More specifically, Quantity A equals the area between –2 standard deviations and the mean of the distribution. In a normal distribution, roughly 34 + 34 + 14 + 14 = 96% of the sample will fall within 2 standard deviations above or below the mean. Limit yourself only to the 2 standard deviations below the mean, then half of that, or 96%÷2 = 48%, falls in this range. In contrast, Quantity B equals the area between –1 standard deviation and +1 standard deviation. In a normal distribution, roughly 34 + 34 = 68% of the sample falls within 1 standard deviation above or below the mean. Since 68% is greater than 48%, Quantity B is greater.
Note that exact figures are not required to answer this question! Picture any bell curve—the area under the “hump” (that is, centered around the middle) is bigger! Thus, it has more members of the dataset (in this case, worms) in it.
