Some grocery stores now offer their customers a free loyalty card that will save money on their purchases. In exchange, the store will keep track of the customer's shopping habits and could potentially sell these data to third parties. A Pew Internet & American Life Project Survey (January 2016) revealed that half of all U.S. adults would agree to participate in the loyalty card program. In a random sample of 250 U.S. adults, let x be the number who would participate in the free loyalty card program.

a. Explain why x is a binomial random variable (to a reasonable degree of approximation).

b. What is the value of p? Interpret this value.

c. What is the expected value of x? Interpret this value.