1. During a calender year, the average electricity cost to run air-conditioning in an office is $985, with a standard deviation of $240. Assume the distribution of electricity costs for offices is unimodal and symmetric.

a) What is the probability an office has an air conditioning electricity cost less than $800?

b) Now, if a random sample of 12 offices was selected, what is the probability that the average air conditioning electricity cost, for this sample, is less than $800?

c) Briefly explain the differences in your answers to part a) and part b).

d) Now, you are told that the population standard deviation is not known. What is the value of the population standard deviation, if the population mean is $985, the sample is size 12,and 75.8% of average electricity costs are less than $1000?

2. A new stock broker in a city, has offered free initial consultations to new clients. The stock broker wants to estimate the proportion of new clients that return after the free initial consultation. Of the 75 randomly sampled new clients, 60 returned.

In this question, use a MINIMUM OF 4 DECIMAL PLACES in all your calculations.

a) What is the value of the sample proportion of clients who return? Please give your value to 4 decimal places.

b) Check conditions for proportions.

c) Construct and interpret a 90% confidence interval for the population proportion. SHOW BRIEF WORKINGS TO SUPPORT YOUR ANSWER.

3.Suppose daily sales revenue for an online store has been, on average, $8000. The owner of the store believes that daily sales revenue has been decreasing. He collects a random sample of 15 recent days of sales revenue and finds an average of $6800 with a standard question deviation $2500. Assume the conditions are satisfied, and do NOT need to be checked.

a) Write the hypotheses to test the online store owner's belief.

b) Give the calculated test statistic value for this test.

c) Give the critical value for this test, at a level of = 0.10.

d) Give your decision.

e) Give your conclusion, in the context of this question.

f) Briefly explain if your decision changes if you were now told to use = 0.05.