Question

The management of a supermarket wants to adopt a new promotional policy of giving a free gift to every customer who spends more than a certain amount per visit at this supermarket. The expectation of the management is that after this promotional policy is advertised, the expenditures for all customers at this supermarket will be normally distributed with a mean of

$
80
and a standard deviation of
$
12.12
. If the management decides to give free gifts to all those customers who spend more than
$
100
at this supermarket during a visit, what percentage of the customers are expected to get free gifts?

Answer 1

The described situation represents a normal distribution.
For a normally distributed distribution, P(X < x) = P(z < (x - mean) / standard deviation))
P(x > 100) = 1 - P(z =< 100) = 1 - P(z < (100 - 80) / 12.12) = 1 - P(z < 1.6502) = 1 - 0.95055 = 0.04945 = 4.9%

Therefore, the required percentage of the customers expected to get free gifts is 4.9%.