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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # A random variable Y is normally distributed with a mean of 2  Question banks Downloads My Bookmarks Reviews Important topics
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A random variable Y is normally distributed with a mean of 2 [#permalink]
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Question Stats: 70% (00:41) correct 29% (00:57) wrong based on 219 sessions
A random variable Y is normally distributed with a mean of 200 and a standard deviation of 10.

 Quantity A Quantity B The probability of the eventthat the value of Y isgreater than 220 $$\frac{1}{6}$$

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

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[Reveal] Spoiler: OA

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Eddie Van Halen - Beat it R.I.P. Founder  Joined: 18 Apr 2015
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Re: A random variable Y is normally distributed with a mean of 2 [#permalink]
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Solution

The mean is 200 and the SD is + 10 or - 10 from the mean. As such , we do have a probability that ranging from 190 to 210. In total 20 numbers on our number line.

From this, we do have $$\frac{1}{20}$$ of probability. This quantity is $$<$$$$\frac{1}{6}$$

The best answer is $$B$$

Alternative solution Another approach to this problem is to draw a normal curve, or “bell-shaped curve,” that represents the probability distribution of the random variable Y, as shown.

The curve is symmetric about the mean 200. The values of 210, 220, and 230 are equally spaced to the right of 200 and represent 1, 2, and 3 standard deviations, respectively, above the mean. Similarly, the values of 190, 180, and 170 are 1, 2, and 3 standard deviations, respectively, below the mean. Quantity A, the probability of the event that the value of Y is greater than 220, is equal to the area of the shaded region as a fraction of the total area under the curve. i.e. the probability of the event that the value of Y is greater than 220 must be less than 5%, or $$\frac{1}{20}$$ and this is certainly less than $$\frac{1}{6}$$ The correct answer is $$B$$.
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Eddie Van Halen - Beat it R.I.P.

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Re: A random variable Y is normally distributed with a mean of 2 [#permalink]
Hey dears
unfortunately i tried hard to understand any of your approaches but, it doesn't work(
if there is more explanation please !
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Re: A random variable Y is normally distributed with a mean of 2 [#permalink]
Could you also say that the shaded region is 2.5% chance of the event happening since its between M+2D and M+3D. If so, the answer would be A. Thanks for the clarification. Retired Moderator Joined: 07 Jun 2014
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Re: A random variable Y is normally distributed with a mean of 2 [#permalink]
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Runnyboy44 wrote:
Could you also say that the shaded region is 2.5% chance of the event happening since its between M+2D and M+3D. If so, the answer would be A. Thanks for the clarification.

No 2.5% chance mean Quantity A is $$\frac{2.5}{100}$$ and Quantity B is $$\frac{1}{6}$$.
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Re: A random variable Y is normally distributed with a mean of 2 [#permalink]
May I know why "the probability of the event that the value of Y is greater than 220 must be less than 5%, or 1/20"? Retired Moderator Joined: 07 Jun 2014
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Re: A random variable Y is normally distributed with a mean of 2 [#permalink]
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Runnyboy44 wrote:
May I know why "the probability of the event that the value of Y is greater than 220 must be less than 5%, or 1/20"?

You have to rememer this graph.

Attachment: norm.png [ 100.5 KiB | Viewed 18623 times ]

You can only have probability in ranges of numbers in this case. This is very important as opposed to discreet events having probability like a coin toss or a dice roll. When we talk about events that are continuous they are represented as the graph above.

For example probability of getting a number between mean + 2 standard devation ($$\mu + 2\sigma$$) and mean + 3 standard devation ($$\mu + 3\sigma$$) is 2.14%.

Or if you picked the numbers 100 times you would get a number between $$\mu + 2\sigma$$ and $$\mu + 3\sigma$$ is 2.14 times.
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Re: A random variable Y is normally distributed with a mean of 2 [#permalink]
Runnyboy44 wrote:
May I know why "the probability of the event that the value of Y is greater than 220 must be less than 5%, or 1/20"?

This problem is based on normal distribution .Its better to remember those percentages as question in gre will be direct basing on them. Intern Joined: 29 Jun 2018
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Re: A random variable Y is normally distributed with a mean of 2 [#permalink]
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220 will be two SD above the mean.

So the probability will be 2% = 1/50

So we are comparing 1/50 and 1/6.

B is the answer Intern Joined: 28 Aug 2018
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Re: A random variable Y is normally distributed with a mean of 2 [#permalink]  Intern Joined: 27 Aug 2018
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Re: A random variable Y is normally distributed with a mean of 2 [#permalink]
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sandy wrote:
Runnyboy44 wrote:
May I know why "the probability of the event that the value of Y is greater than 220 must be less than 5%, or 1/20"?

You have to rememer this graph.

Attachment:
norm.png

You can only have probability in ranges of numbers in this case. This is very important as opposed to discreet events having probability like a coin toss or a dice roll. When we talk about events that are continuous they are represented as the graph above.

For example probability of getting a number between mean + 2 standard devation ($$\mu + 2\sigma$$) and mean + 3 standard devation ($$\mu + 3\sigma$$) is 2.14%.

Or if you picked the numbers 100 times you would get a number between $$\mu + 2\sigma$$ and $$\mu + 3\sigma$$ is 2.14 times.

Thank you for the explanation. If one understands this principle, there is nothing hard GRE Instructor Joined: 10 Apr 2015
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Re: A random variable Y is normally distributed with a mean of 2 [#permalink]
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Carcass wrote:
A random variable Y is normally distributed with a mean of 200 and a standard deviation of 10.

 Quantity A Quantity B The probability of the eventthat the value of Y isgreater than 220 $$\frac{1}{6}$$

Here's what a normally distributed population looks like: The values on the bottom of the diagram represent the number of standard deviations from the mean.

Since the mean of the population of y-values is 200, we can add that to our diagram Since the standard deviation is 10, we can see that a value of 220 is TWO UNITS OF STANDARD DEVIATION above the mean Our diagram tells us that 2% of the y-values will be greater than 220

In other words, P(selected y-value is greater than 220) = 2% = 2/100 = 1/50

We get:
QUANTITY A: 1/50
QUANTITY B: 1/16

Quantity B is greater

Cheers,
Brent
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If you enjoy my solutions, you'll like my GRE prep course.  Re: A random variable Y is normally distributed with a mean of 2   [#permalink] 14 Feb 2019, 11:32
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