6 Customers at a supermarket can pay at a checkout either by cash, debit card or credit card.
- The probability that a customer pays by cash is 0.22 .
Calculate the probability that exactly 2 customers from a random sample of 24 customers pay by cash.
- The probability that a customer pays by debit card is 0.45 .
Determine the probability that the number of customers who pay by debit card from a random sample of \(\mathbf { 4 0 }\) customers is:
- fewer than 20 ;
- more than 15 ;
- at least 12 but at most 24 .
- The random variable \(W\) denotes the number of customers who pay by credit card from a random sample of \(\mathbf { 2 0 0 }\) customers.
Calculate values for the mean and the variance of \(W\).
[0pt]
[3 marks]