Maths Maths Maths

 Okay I'm back with the mark sceme now!

b)i) I was right, it is 0 for the answer. This is because when you are calculating probabilities with a normal distribution (or any continuous one) you have to work out an area under the graph, so it has to be less than, more than, or between two values, since jst a line on a graph doesnt have an area. 

ii) I was right with what I first started saying. Do 1-probability from former question, then do it to the power 6.

iii)Now the seccond way i was trying to do the other one is what you do for this one. You want to work out the distribution for Xbar, which is (using central limit theorum and because it was a normal distribution anyways) a normal distribution. So Xbar~N(original mean,varience divided by 6) since n=6 days. Now do the same as in the first question, using them new values to get a Z value, so then you are working out P(Xbar < 60).

Okay the first bit is just a normal distribution. you have X~N(65,202). Draw a picture!

You then need to translate that into Z instead of X, using the equation: Z=(X - mean) divided by (standard deviation).

Once you have the Z value you can use the tables in the back of the book to find the first probability.

The second one, you need to think about more since the book only has less than probabilities while that is a more than one. Use the fact that hte total area inder the graph is equil to 1 to help.

Now onto b.

I am a bit confised by all this. I'm warnign you that i am just taking some random guesses right now, since I wanna go watch this mermaid programme :/ Ill look into it better when i come back and look at the mark scheeme and all that...

i) since there is only one mark I am tempted to say the answer is 0. but im not atually sure :/ (I fail right now)

ii) Now this probably something to do with question a) ii) since they both involve 60. I would say that you need to work out the probability she compleates it in less than 60 mins on one day. (1-probability worked out in other question) then times that by itself 6 times.