A type of new car is offered for sale with 4 option packages. A customer can buy any number of these, from none to all 4. A manager proposes the null hypothesis that customers pick packages at random, implying the number of packages bought by a customer should be binomial with n = 4. This table shows the number of packages chosen by 400 customers. Find the

(a) Binomial parameter p needed to compute the expected counts.
(b) Estimated probability that a customer picks one option.
(c) Degrees of freedom for x2.
(d) x2.
(e) p-value for testing H0.

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Customers 20 90 140 120 30