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The lifetime of all the batteries produced by a certain company in a year have a distribution that is symmetric about

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The lifetime of all the batteries produced by a certain company in a year have a distribution that is symmetric about

by BTGmoderatorDC » Wed Jul 08, 2020 7:47 pm

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The lifetime of all the batteries produced by a certain company in a year have a distribution that is symmetric about the mean m. If the distribution has a standard deviation of d, what percent of the distribution is greater than m+d?

(1) 68 percent of the distribution lies in the interval from m-d to m+d, inclusive
(2) 16 percent of the distribution is less than m-d



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Re: The lifetime of all the batteries produced by a certain company in a year have a distribution that is symmetric abou

by deloitte247 » Fri Jul 10, 2020 8:27 am

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Given that the distribution is symmetric about the mean m, this means that 50% of the distribution is above and below the mean
- Distribution also has a standard deviation of d

Statement 1 => 68% of the distribution lies in the interval from m - d to m + d, inclusive
100% - 68% = 32%
32% is less than m-d and more than m+d
As the distribution is symmetric about the mean 50% of 32% would be more than m+d
i.e 50/100 * 32 => 1/2 * 32
= 16%; would be greater than m+d
Statement 1 is SUFFICIENT

Statement 2 => 16% of the distribution is less than m-d
Recall that 50% of the distribution is above and below the mean, so if 10% of the distribution is less than m-d then 10% will be greater than m+d
Statement 2 is also SUFFICIENT

Since each statement alone is SUFFICIENT,
Answer = D
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