The Red   Lobster restaurant chain regularly surveys its customers.  On the   basis of these surveys, the management of the chain claims that 75% of its   customers rate the food as excellent.  A consumer testing service   wants to examine the claim by asking 460 customers to rate the   food.  What is the probability that less than 70% of customers rate   the food as being excellent?   Develop a 99 percent confidence   interval over the value of the population proportion of customers who view   the food as being excellent.  Can the claim be justified based on   this evidence at the 1 percent significance level?    

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