### CFA Practice Question

There are 434 practice questions for this study session.

### CFA Practice Question

As part of a promotion for a new type of cracker, free trial samples are offered to shoppers in a local supermarket. The probability that a shopper will buy a packet of crackers after testing the free sample is 0.20. Different shoppers can be regarded as independent trials. Let X be the number among the next 100 shoppers who buy a packet of the crackers after tasting a free sample. The probability that fewer than 30 buy a packet after tasting a free sample is approximately ______.

A. 0.20
B. 0.9938
C. None of the above

X, the number among the next 100 shoppers who buy a packet of the crackers after tasting a free sample, has approximately an N(20, 4) distribution. You need to evaluate P(X <= 30), which equals 0.9938.

User Comment
humphrey do I have a Z table to look up during exam?
murli From where you got 4?
katybo looks like binomial to me.
LondonBoy mmm... also not sure where 4 came from?
nsmwaura Yikes... this scares me
lawrence 4 is the standard deviation. [100 x 0.2 x (1-0.2)]^(1/2) = 4. N(m, std) is the convention for standard normal distribution with m as the mean adn std as the standard deviation.
danlan Binomial will be approximated by normal distribution.
cwrolfe Yes you do need a z-table...or you can extrapolate...

1st calculate mean = p(x) times n = .2 x 100 = 20

2nd calculate std. deviation (see "lawrence" above) = 4

3rd convert 30 to a z-value above mean = (30-20)/4 = 2.5 std deviations

4th, look up this z-value on a table or know that 99% of values of x will fall within +/- 2.58 std deviations of the mean (it will be slightly less than 99% because of our 2.5 z-value, but close enough)

5th take half of this amount as our probability above the mean of 20, and you get 49.5%

6th add that to the 50% probability below the mean and you get 99.5%, plus we know its a little lower than this because of our assumption is step 4.
khush Yes, you get a book of tables in the exam
bobert Crwolfe, I think you added an extra step.
Do steps 1, 2, 3.
For 4, 2.5 on the Z-table = .4938
Then recognize that the Z table gives values from 0 to 4, not negatives. Since this is a positive Z-score simply add the 50% from the below 0, or the negative Z-score side which is completely encompassed. p(x)= x<30.

That gets you the exact answer. Your way also works though as none of the other answers were even close.
Tomcat82 mean of binomial random variable=np=100*0.2=20.

variance of binomial random variable = np(1-P), where n=100, p=.2. var=100*0.2*0.8=16.

Now you want the standard deviation, which is (16)^(1/2)=4. Now the z-score=(x-M)sd, which is (30-20)/4=2.5.

Look up the probablility for the z-value on the z-table, which is equal to 0.9938
StanleyMo This question include binomial theorem and standard normal distribution. nice question.
Yurik74 Using binomianl got pretty much the same result 0.9948.
JKiro good question... thanks Tomcat82
bantoo great explanation tomcat!
gulfa99 Tomcat82...i am lost..100*0.2*0.8
where did 0.8 come from?
gulfa99 oops i got it..thanks
Kaloyan Tomcat82, excellent explanation!
sgossett86 Gulfa .8 = 1-P from multiple variable bernoulli formula to get variance. sigma^2=np(1-p)
Rachelle3 I do it like Tomcat82 but I find this power ^ 0.5 thing weird just do sq root of 16 = 4 any time you see power ^ half or 0.5 or 1/2 like I have seen on this site it is BETTER to sq root same thing OK?
Do not make it longer than it needs to be I am sure you have this button on your calculators!!! SQ ROOT PLZ
ashish100 Rachelle3 most people use that sq root function i'm sure. its just easier to type ^.5 thatn whatever the sign for sq root is on here. see, i dont even know what the sign for sq root is on here.