(PLEASE SHOW THE CALCULATIONS IN EXCEL SHEET - THANK YOU!)

An anti-virus software company interviews company purchasing officers to find out how much each intends to spend next year on computer security per PC. Each interview costs the software company $100. After 20 randomly selected interviews, the sample mean intended security expenditure is $40 and the estimated standard error is $15.

1. The software company is dismayed that the estimated standard error is so high. About how many additional interviews would it take to reduce the standard error to about $9?

2. About what proportion of the population of purchasing officers intends to spend more than $60 per PC on security? Does your answer change if you know that the amounts that the population of purchasing officers intend to spend are normally distributed?

3. Suppose that a new survey of 50 randomly selected purchasing officers is to be done. Suppose we call the survey result "accurate enough" if the sample mean differs from the population mean by less than $10. What is the approximate probability that the survey result will be accurate enough, if the population mean amount to be spent on security per PC is actually $60 and the population standard deviation is actually $30?

Explicitly state any additional assumptions that you believe you must make to answer this.