Question

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?

The Central Limit Theorem not only has the magic power to turn a sample mean Xbar into a normal variable but also has the power to turn the sample proportion variable Pbar into a normal variable. Pbar ~N(π,SE) where SE = sqrt(π*(1-π)/n)

QUESTION 1 Population proportion π = 0.75; sample size = 70 What is the sample proportion's Standard Error? Tip: Sqrt(π*(1-π)/n) 5 decimals. (ex. if the answer is 7.8946%, write as 0.07895

QUESTION 2 The same question: Population proportion π = 0.75; sample size = 70 What is the Z-value if less than 70% rate the food as excellent? Tip: Pbar = 0.70 Z = (Pbar - π)/Standard Error 3 decimals.

Answer 1

QUESTION 1 Population proportion π = 0.75; sample size = n = 70 What is the sample proportion's Standard Error se()?

The same question: Population proportion π = 0.75; sample size = 70 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?

Which is same as P(Z < -0.966) = 0.1670