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 70 customers to rate the food. What is the probability that less than 70% rate the food as excellent?

What is the sample proportion's Standard Error?

What is the Z-value if less than 70% rate the food as excellent?

What is the probability that less than 70% rate the food as excellent?

Now, the company increased the sample size to 300 customer survey,

Same questions: Population proportion = 0.75; sample size = 300

What is the probability that less than 70% rate the food as excellent?