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# Z-Table during the exam

#### Ludwma

##### Member
Subscriber
Hi David,

In the FRM handbook there is the following question:
"Assume that a random variable follows a normal distribution with a mean of 80 and standard deviation of 24. What is the probability that this random variable is not between 32 and 116?"

I think that it is required the z-table in order to answer to this question. Am I wrong? If not, is the z-table provided during the exam?

Thanks,

FS

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi FS,

Yes, it is a good example of a question that will NOT expect you to have memorized the tail probabilities associated with a normal deviate (e.g., -2.0 or +1.5). My recommendation is to memorize four:
• One-sided 95% and 99% standard normals: N(-1.645) = 5% and N(-2.33) = 1%. Because all normal VaR questions will use these. Necessary.
• Two-sided 95% and 99% standard normals: N(-1.96) =2.5% so 5% in two-tails, and N(-2.58) = 0.005, so 1.0% in two-tails. Maybe not necessary but recommended as typical significance test (e.g., is regression slope coefficient significant) will use these. Recommended.
For anything else, including your example, GARP will provide the information (table or table extract), here was their recent response on their facebook page:

Question to GARP on FB: "Do we get a formula sheet for the exam?"
"GARP's Answer: If a question requires information from a specific distribution table, that information will be provided. With respect to “Quantitative Analysis” topics outlined in the 2011 Study Guide, candidates are not expected to memorize formulas of distributions, but should understand when it is appropriate to use a particular type of distribution. The two approved calculators [sic: more than two calculators are approved] are capable of performing any required present value and future value calculations. Best regards, GARP FRM" -- See here.
I hope that helps, thanks,

Last edited:

#### Alex_1

##### Active Member
Just got to this thread via a link. I think in the post above it should state:
"N(-1.645) = 5% and N(-2.33) = 1%" instead of "N(-1.645) = 5% and N(-2.33) = 99%"
Just for future candidates who stumble upon this. #### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Thank you, again, @Alex_1 !

#### Jo_

##### Member
Subscriber
two things worth to notice:

- GARP gave a z-table with negative z-values only for the may 2014 exam. So be sure you understand and know how to extract from that positive z-values (P[Z<-z] = 1- P[Z<z]
- GARP asked for a 90% VaR in one of the questions, be sure to know how to find the appropriate z-score (it's something around 1,3 from memory)

#### tosuhn

##### Active Member
Hihi, how do i get the one sided p-value of 13.5% for ques 3 under R.10P1.T2 pg 91.

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @tosuhn as the question (following Miller) implies I think, the exam is unlikely to ask you to compute a p-value. But you still want to understand how to retrieve it. I used T.DIST(1.1336, 9 df, TRUE = cdf) ~= 86.5% or T.DIST.RT(1.1736, 9) ~= 13.5%. But you just want to understand what it means. I think a good way to see this is to recognize the upper row in the lookup table as effectively p-values. For example, at 9 df, given a t-stat of 1.383, the one-sided p value is 0.10 or 10%. In words, 10% is the area under the curve in the right tail which represents the rejection region. Interpolation between these values--which i highlighted in yellow--should correspond to (1-86.5%). I hope that helps! #### sharman.jamie

##### Member
Hi, this is a pretty old thread but is it possible you can make available on the site somewhere a typical table we will be given? I'm finding these questions very difficult because I don't know what form of each table will be available. My question applies to z values, critical t values (especially how these differ with different degrees of freedom), F statistics etc.

#### emilioalzamora1

##### Well-Known Member
Hi @sharman.jamie,

can you please go the GARP website and download one official sample exam. This sample exam contains exactly the tables you will see on exam day. Hope this helps.

#### sharman.jamie

##### Member
Hi @sharman.jamie,

can you please go the GARP website and download one official sample exam. This sample exam contains exactly the tables you will see on exam day. Hope this helps.

Perfect thanks, I can see that you get the full z table and relevant snippets of tables elsewhere

#### anisapassfrm

##### New Member
so for the exam, GARP only provides Z-table?
What about t,f, X^2 distribution table?

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @anisapassfrm Yes GARP provides standard normal lookups (aka, Z table) on the exam. The other tables to which you refer will not be provided (or are unlikely to be provided) except on a need-to-know basis. Obviously GARP cannot expect you to have chi-squared values memorized , although you should know that about 2.0 is a "sweet spot" for the student's t (a test of sample mean leads automatically to a hypothesis rejection for any high test statistic ... in many cases, a sample mean test does not require any lookup!).

See GARP's FRM FAQ here at https://www.garp.org/#!/frm/frequently-asked-questions i.e.,
"Z-Table Information:
A standard table presenting the values for the cumulative distribution function (CDF) of the standard normal distribution (“z-table”) is provided, as is other relevant information pertaining to the CDFs of other probably distributions (F, chi-square, etc.) where necessary and applicable. Memorization of CDF values is therefore not expected. A list of common abbreviations used throughout the Exam is also provided."

#### renewijaya

##### New Member
It is possible to calculate it using ZTable. Although it need to be provided, otherwise hard to memorize it during the exam. Hopefully we can find the alternative way for the solution of the data sets.

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