Rounding off

[kartik_newpro]

Chp 8 - Q. 8.7

What is the approximate probability that the mean of a sample of 10 observations from a Beta(10,10) random variable falls between 0.48 and 0.52?

Here the mean = 0.5 and variance = 0.011904761

I approximated this as N(0.5,0.012/10) and got the answer 0.43629

The solution in the study material approximated N(0.5,0.01190/10) and their answer is 0.43794.

Would my answer be considered wrong? If yes then how do I figure out when to round off and when to not.

This has happened many a times throughout my CT3 course. I apply the concepts and formulas properly but end up getting inaccurate answers.

 

[John Lee]

Are you using linear interpolation when calculating your normal probabilities?

 

[kartik_newpro]

Yes I do. But does that matter? Because problem here occurred because I rounded off the variance.

 

[John Lee]

Because problem here occurred because I rounded off the variance.

Since you rounded it to only 2 SF you can only hope for your answer to be correct to 2 SF. Examiners look at at least 3 SF. So in this case you would not get the marks.

The best thing to do is to store the full answer in your calculator's memories and use those when standardising.