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.

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