Question

Andy is a restaurant owner. He believes 70% of his customers are satisfied with the food quality of his restaurant. From a random sample of 83 customers, what are the following probabilities? (Round to 2 decimal places for all z-values and round all other answers to 4 decimal places, if needed.)

Answer 1

Seventy percent of customers arrive within 2.41 minutes of the previous customer. Whether an exponential distribution is reasonable for this situation depends on various factors.

Step-by-step explanation:

e. Seventy percent of the customers arrive within 2.41 minutes of the previous customer. To find the 70th percentile, we can use the formula: z = (x - μ) / σ, where x is the value at the percentile, μ is the mean, and σ is the standard deviation. Rearranging the formula, we have x = z * σ + μ. In this case, z = 0.524 (corresponding to the 70th percentile), μ = 2.41 minutes, and σ is not given. Therefore, we cannot calculate the exact value of x.

f. Whether an exponential distribution is reasonable for this situation depends on the nature of customer arrivals. An exponential distribution assumes that the time between arrivals follows an exponential decay pattern, which may not be the case in reality. Other factors, such as customer behavior and external influences, can affect the distribution of arrival times.