Suppose the distribution of home sales prices has mean k300, 000 and standard deviation of k50, 000.
(i) Determine the price range in which at least 75% of the houses sold.
[4 Marks]
(ii) Determine the minimum percentage of the houses that should sell for
prices between k150, 000 and k450, 000. [4 Marks]
(iii) Determine the minimum percentage of the houses that should sell for
prices between k170, 000 and k430, 000

Given:

Mean,

Standard deviation,

The Chebyshev theorem will be used for the solution of the given query,

i.e.,

(i)

⇒

The lower limit will be:

=

=

=

The upper limit will be:

=

=

=

hence,

The 75% houses sold are between:

⇒ (200000, 400000)

(ii)

⇒

By putting the values, we get

now,

⇒

              (%)

hence,

88.88% houses sold between 150000 and 450000.      

(iii)

⇒

By putting the values, we get

now,

⇒

              (%)

hence,

85.21% houses are sold between 170000 and 430000.

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ab will be equal to