The area of each shop space in a newly constructed regional shopping mall is normally
distributed with a mean of 950 square metres and a standard deviation of 30 square metres.
a. If the random variable X is the area of the shop, identify the distribution of X and state the
value/s of its parameter/s.
b. A local business is considering moving their business into the one of the shops in the new
mall. She requires a space which has an area of at least 1000 square metres. Calculate (using
the appropriate statistical tables) the probability of there being a space suitable for her
business in this new mall.
c. A take away food franchisee can operate satisfactorily within an area of between 900 and
1100 square metres. Calculate (using the appropriate statistical tables) the probability there
will be a suitable space for this business.
d. Five percent of all shops in this new mall are larger than x square metres. Calculate the
value of x.
e. Verify your answers to parts b., c. and d. using the appropriate Excel statistical function
and demonstrate you have done this by including the Excel formula used. (3 marks)
f. A random sample of twenty shops in this mall is selected. State the type of distribution and
the value/s of the parameter/s for the mean of this sample.
g. Calculate (using the appropriate statistical tables) the probability that the average area of
this sample is less than 940 square metres.