In the problem I am given :

n = 8 (sample size)

The random variable follows a normal law with a standard deviation of 0.25

The problem also states that we need to reject [tex]H_0[/tex] if or

I need to find the probability of a type I error.

What I've tried so far: (alpha represents my Type I error)

So I tried to start and find the probability of not in that interval.

which gives me

when I plug my numbers and isolate , i get

It seems to me that this value of Z can't be right since my table only goes to a maximum of 3.09.

As for the rest of the problem, I could use a tip or two about how to find P(u=5) and how to calculate the conditionnal probability.

Thanks