Cashier records from the last year show that 35% of all Ralph's grocery store customers use a ...

  

Cashier records from the last year show that 35% of all Ralph's grocery store customers use a previously-obtained Ralph's discount card upon checkout. Management suspects the percentage of actual cardholders is higher because some customers may not use their Ralph's card during every visit. They decide to sample random customers who enter the store, and ask them if they have a Ralph's card. Suppose they solicit 400 customers one day, and find that 160 of them have a Ralph's card.   
 

Assuming for a moment that 35% of all Ralph's customers have a discount card, what is the probability of getting a sample proportion at least this big?
 

(a) Find the mean of the distribution. Round your final answer to two decimal places
 

(b) Find the standard error of the distribution. Round your final answer to two decimal places
 

(c) Calculate the probability. Round your final answer to two decimal places