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###### Math · Mathematics
Question details

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

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.