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Part 2 Q&A Bank. FAO John

J

jimjoachim

Member
Hi.

Regarding question 2.23 part (i)
The question says that the mean and standard deviation are 20 mins and 5 mins respectfully however the solution is using a N(20,5) distribution.

Is this a mistake??

Also the same problem arises in question 2.28 where the linear combination of the normal dists is adding the standard devs of both and not the variances.

Am I missing something completely or is this a mistake?? :confused:

Cheers

James
 
Almost!

jimjoachim said:
Hi.

Regarding question 2.23 part (i)
The question says that the mean and standard deviation are 20 mins and 5 mins respectfully however the solution is using a N(20,5) distribution.

Is this a mistake??

Am I missing something completely or is this a mistake?? :confused:
Click to expand...

No - it is correct (though you had me worried for a bit!)

You are correct in saying that X ~ N(20, 5²)

However, we are doing probabilities for X bar - which for n = 5 has a distribution of:

X bar ~ N(20, 5²/5) = N(20, 5)

The confusion has arisen that the sample size is the same as the standard deviation so when we divide the variance through by n it looks like we're just working with the standard deviation.

Q2.28 is similar.

Clear as mud?
 
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