Question

It has been proven that the bill paid by the customers of a super market follows the Normal distribution with an average of 55.4 euros and a variation of 225.
2A) Calculate the probability of a customer giving a 100 euro banknote to the cashier, he received a change from 30 to 60 euros.
2B) The super market wants to offer a gift to its good customers, that is, to those who exceed an amount. What should this amount be if the supermarket wants to offer this gift to only 4% of its customers?

Answer 1

Let X be the random variable denoting  that the bill paid by the customers of a supermarket

A) If we want the probability of receiving a change from 30 to 60 euros

= probability of bill amount is 40 to 70 euros

= P(40 < X < 70)

=P (Z < 0.973) - P(Z < -1.026)

= 0.8347 - 0.1525

= 0.6822

B)Let K be the amount

So

P(X > K) = 0.04

But from normal distribution table

P(Z > 1,75) = 0.04

So

So K = 81.65

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