Got Part a right, need help getting part b, critical t value

There is a random sample of 1000 members, and the sample mean income, xbar, is 900$. it is also given that mu= $1000 and variance = 10000--squared.

a) Given that u= 1000$, what is the probability of obtaining such a sample mean value?

b) Based on the sample mean, establish a 95% confidence interval for mu, and find out if this confidence interval includes mu = 1000$. IF it does not, what conclusions would you draw.

So I got A, by doing the following

t = X bar - mu/ S/ , so then i got 900-1000/100/31.6 = 100/3/16 = -31.6, and since z< -31.6 tghe probability will be 0.

Okay now for part B, this is where i hit a roadblock.i know for the 95% confidence interval, you have to try to find the critical t values, but the equation is the same. I am wondering how can i get this info based on the data, the answer is 893.8019<mux<906.1981.

Please help! Im so stuck right now.

Re: Got Part a right, need help getting part b, critical t v

Your notation looks bad, but the rest looks fine.

What is the point of that last "squared" on the first sentence?

I think you mean (900-1000)/(100/31.6) whuch is WAY different from what you wrote.

What's the z-score for a 2-sided 95% confidence interval?