Find the spending rejection boundary without over-rounding

A department store reports that average spending per customer over the past six months is $215 with standard deviation $100. During a week-long sales promotion, it takes a random sample of 100 visiting customers and records their spending. It tests at 5% whether the promotion increased average spending.

(i) State, with a reason, whether the test requires assuming normally distributed customer spending.

(ii) State the null and alternative hypotheses. Given that the null hypothesis is rejected, show that the sample mean is greater than $231.45.