1. According to the records of an electric company serving the Bangsar area, the mean electricity consumption for all households during winter is 1650 kilowatt-hours per month. Assume that the monthly electricity consumptions during winter by all households in this area have a normal distribution with a mean of 1650 kilowatt-hours and a standard deviation of 320 kilowatt-hours.

a. Find the probability that the monthly electricity consumption during winter by a randomly selected household from this area is less than 1950 kilowatt-hours.

b. What percentage of the households in this area have a monthly electricity consumption of 900 to 1300 kilowatt-hours?

2. The management of a supermarket wants to adopt a new promotional policy of giving a free gift to every customer who spends more than a certain amount per visit at this supermarket. The expectation of the management is that after this promotional policy is advertised, the expenditures for all customers at this supermarket will be normally distributed with a mean of $110 and a standard deviation of $20. If the management decides to give free gifts to all those customers who spend more than $150 at this supermarket during a visit, what percentage of the customers are expected to get free gifts?

3. A psychologist has devised a stress test for dental patients sitting in the waiting rooms. According to this test, the stress scores (on a scale of 1 to 10) for patients waiting for root canal treatments are found to be approximately normally distributed with a mean of 7.59 and a standard deviation of 0.73.

a. What percentage of such patients have a stress score lower than 6.0?

b. What is the probability that a randomly selected root canal patient sitting in the waiting room has a stress score between 7.0 and 8.0?

c. The psychologist suggests that any patient with a stress score of 9.0 or higher should be given a sedative prior to treatment. What percentage of patients waiting for root canal treatments would need a sedative if this suggestion is accepted?