S2 problem question

It is part C in which I am struggling with - I have looked on the tables for p(x<= 10) for the last value in which it is greater than 0.9, I found this value, but then the final answer on the markscheme correlates to a different value?

Thank you

Look at the percentage points table, i.e: the table right below the normal distribution one in your formula booklet, you'll see that it gives a z value of 1.2816.

I don't really see how this is helping me

Oh, sorry. I assumed it was a normal distribution question without looking at the previous parts.

$\mathbb{P}(C > 10) < 0.1 \iff \mathbb{P}(C \leq 10) > 0.9$.

According to the markscheme, apparently not

Does this help:

Yeah - they were the two values I found, but then in the markscheme the final answer is lambda = 7/4?

Yes, because Charlotte does it over 4 hours. So, really what you've found is $C \sim Po(\mu)$ where $\mu = 7$.

But the random variable $X \sim Po(\lambda)$ is over 1 hour. So $C \sim Po(4\lambda)$, that is: $\mu = 4\lambda$.

Oh yeah... should've realised that

Thank you