BADB1014 Quantitative Methods
Assignment 3
Topic 4 - Normal and Standard Normal Distribution
NORMAL AND STANDARD NORMAL PROBABILITY DISTRIBUTION
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?
BADB1014 Quantitative Methods
Assignment 3
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?
BADB1014 Quantitative Methods
Assignment 3
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?