Statistics Help : Hypothesis Testing

[girlwhoneedsmathhelp]

TL;DR

There's this question and I have worked it out until the end but don't understand why the answer is the answer

Answer :

I understnad why x(< or = ) 2 but I do not understand why we use 16 instead of 17 for the second range? When P(X>=16) > 0.005(which is the level of significance). Thank you for all the help given :)

 

[mfb]

"As close as possible to 0.005".

0.0064 is closer to 0.0050 than 0.0021.

 

[hutchphd]

None of this is exact of course but I believe I was taught to default to the more conservative number when rounding to an integer value. This is not what the question prescribes but seems more prudent to me ( the significance level will be 1% or less). I am not sure which is the norm!