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The length of bolts made in factory Z is normally distribute

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GRE Prep Club Legend
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Joined: 07 Jun 2014
Posts: 4810
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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The length of bolts made in factory Z is normally distribute [#permalink] New post 29 Jul 2018, 04:45
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Question Stats:

66% (00:57) correct 33% (02:00) wrong based on 15 sessions
The length of bolts made in factory Z is normally distributed, with a mean length of 0.1630 meters and a standard deviation of 0.0084 meters. The probability that a randomly selected bolt is between 0.1546 meters and 0.1756 meters long is between

(A) 54% and 61%.
(B) 61% and 68%.
(C) 68% and 75%.
(D) 75% and 82%.
(E) 82% and 89%.
[Reveal] Spoiler: OA

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Re: The length of bolts made in factory Z is normally distribute [#permalink] New post 30 Sep 2018, 08:48
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Answer is D.

First do away with the decimals.
Mean = 1630, SD = 84

Given sizes = 1546 and 1756.

1546 = 1630 - 84 Therefore it's 1 SD to the left of the mean = 34% probability

1756 = 1630 + 126 Therefore its > 1 SD but < 2 SD hence 34% + something less than 14%

Add the probabilities = 34 + 34 + <14% = < 82 %

D is the most accurate.
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Re: The length of bolts made in factory Z is normally distribute [#permalink] New post 10 Jan 2019, 19:18
Quote:
The range is 1 std dev below and 1.5 std dev above the mean.

The probability that it is within 1 std dev of the mean is about 68%, so we know it is above that and hence not (a) or (b).

The probability that it is within 2 std dev of the mean is about 95%. So that puts (95%-68%)/2 in each lobe between 1 std dev and 2 std dev, or about 13.5%.

Between -1 std dev and +2 std dev would be 68% + 13.5% = 81.5%. So that rules out (e).

We know that significantly more than half of that 13.5% is between 1 std dev and 2 std dev, which means that the answer is noticeably more than 74.5%. That pretty well rules out (c).

Hence the only answer that seems plausible is (d).

Figure that about 2/3 of that is between 1 std dev and 1.5 std dev and that gets another 9% give or take, bringing it to about 77%.
Re: The length of bolts made in factory Z is normally distribute   [#permalink] 10 Jan 2019, 19:18
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The length of bolts made in factory Z is normally distribute

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