It is currently 22 Nov 2019, 15:57

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# A random variable Y is normally distributed with a mean of 2

Author Message
TAGS:
Founder
Joined: 18 Apr 2015
Posts: 8831
Followers: 176

Kudos [?]: 2058 [1] , given: 8149

A random variable Y is normally distributed with a mean of 2 [#permalink]  14 Jan 2016, 07:38
1
KUDOS
Expert's post
00:00

Question Stats:

71% (00:43) correct 28% (00:37) wrong based on 121 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.

Practice Questions
Question: 9
Page: 331
Difficulty: medium
[Reveal] Spoiler: OA

_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos
GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.

Founder
Joined: 18 Apr 2015
Posts: 8831
Followers: 176

Kudos [?]: 2058 [0], given: 8149

Re: A random variable Y is normally distributed with a mean of 2 [#permalink]  14 Jan 2016, 10:03
Expert's post
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 $$B$$.
_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos
GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.

Intern
Joined: 24 May 2016
Posts: 33
Followers: 0

Kudos [?]: 10 [0], given: 22

Re: A random variable Y is normally distributed with a mean of 2 [#permalink]  13 Dec 2016, 12:40
Hey dears
unfortunately i tried hard to understand any of your approaches but, it doesn't work(
if there is more explanation please !
Intern
Joined: 12 Aug 2018
Posts: 9
Followers: 0

Kudos [?]: 3 [0], given: 3

Re: A random variable Y is normally distributed with a mean of 2 [#permalink]  08 Sep 2018, 20:48
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
Posts: 4808
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 145

Kudos [?]: 2290 [1] , given: 393

Re: A random variable Y is normally distributed with a mean of 2 [#permalink]  09 Sep 2018, 01:33
1
KUDOS
Expert's post
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 $$\frac{1}{6}$$.
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Intern
Joined: 12 Aug 2018
Posts: 9
Followers: 0

Kudos [?]: 3 [0], given: 3

Re: A random variable Y is normally distributed with a mean of 2 [#permalink]  10 Sep 2018, 22:56
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
Posts: 4808
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 145

Kudos [?]: 2290 [4] , given: 393

Re: A random variable Y is normally distributed with a mean of 2 [#permalink]  11 Sep 2018, 05:18
4
KUDOS
Expert's post
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 9579 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.
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Intern
Joined: 15 Sep 2017
Posts: 34
Followers: 0

Kudos [?]: 16 [0], given: 2

Re: A random variable Y is normally distributed with a mean of 2 [#permalink]  11 Sep 2018, 06:30
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
Posts: 10
Followers: 0

Kudos [?]: 9 [1] , given: 0

Re: A random variable Y is normally distributed with a mean of 2 [#permalink]  11 Sep 2018, 11:01
1
KUDOS
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.

Intern
Joined: 28 Aug 2018
Posts: 1
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: A random variable Y is normally distributed with a mean of 2 [#permalink]  12 Sep 2018, 13:02
Intern
Joined: 27 Aug 2018
Posts: 36
Followers: 0

Kudos [?]: 17 [1] , given: 7

Re: A random variable Y is normally distributed with a mean of 2 [#permalink]  14 Sep 2018, 00:57
1
KUDOS
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
Posts: 2572
Followers: 91

Kudos [?]: 2749 [3] , given: 40

Re: A random variable Y is normally distributed with a mean of 2 [#permalink]  14 Feb 2019, 11:32
3
KUDOS
Expert's post
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
_________________

Brent Hanneson – Creator of greenlighttestprep.com

Re: A random variable Y is normally distributed with a mean of 2   [#permalink] 14 Feb 2019, 11:32
Display posts from previous: Sort by