Portion of Customers

The amount spent per month by a segment of credit card users of a bank has a mean value of 12000 and a standard deviation of 2000. Calculate the proportion of customers who are spending between 8000 and 16000.

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Let's use Chebhshev’s theorem, to calculate the percentage of population between 8000 and 16000.

Mean = 12000

Standard Deviation = 2000

Lower Bound = Mean — K * Standard Deviation = 8000

12000 — K * 2000 = 8000

-2000K = -4000

K = 2

Same K value will be calculated from upper bound

Upper Bound = Mean + K * Standard Deviation = 16000

12000 + K*2000 = 16000

2000K = 4000

K = 4000 / 2000

K = 2

As per Chebyshev’s

=1–1/K**2

=1–1/(2**2)

=1–1/4

=3/4

=0.75

75% of the population exists between 8000 and 16000