Cashier records from the last year show that 60% of all Grayson's Grocery store customers use a previously-obtained Grayson's discount card upon checkout. Management suspects the percentage of actual cardholders is higher because some customers may not use their Grayson's card during every visit They decide to sample random customers who enter the store, and ask them if they have a Grayson's card.

Suppose they solicit 400 customers one day, and find that 250 of them have a Grayson's card. Assume that 60% of all Grayson's customers have a discount card, what is the probability of getting a sample proportion of at least 250 / 400=0.625?

Solution Preview

In this problem, we shall apply normal approximation to binomial distribution.

Sample Proportion,p =0.6
q=1-p=0.4
Sample ...

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