Problem 1: Waiting time collected randomly from 100 customers in a bank is given in the following table, given that the waiting time follows a normal distribution.

Waiting time (minutes) 0 5 10 15

Number of customers 15 35 40 10

1. Find the 90% confidence interval for the mean of waiting time of the bank's customers.

2. Explain in details, what is the trade-off if we choose the level of confidence at 99% instead of at 90% when constructing a confidence interval?

3. Test if the mean of the waiting time is smaller than 10 minutes.

4. Explain what type of error you may commit when answering the previous question? Be specific in the context, any consequences if you commit that error?

Problem 2: The distribution of a store's daily profit (mill VND) and the day's weather are given in the following table.

A

A -5 15 25

B

Rainy 0.1 0.1 0.05

Not rainy 0.05 0.2 ?

1. Find the probability for the firm's profit to be 15%, given that the day is not rainy.

2. Find the expected value of the firm's profit.

3. Find the expected value of the firm on a rainy day.