Discuss the below:
When a pizza restaurant's delivery process is operating effectively, pizzas are delivered in an average of 45 minutes with a standard deviation of 6 minutes. To monitor its delivery process, the restaurant randomly selects five pizzas each night and records their delivery times.
a. For the sake of argument, assume that the population of all delivery times on a given evening is normally distributed with a mean of μ = 45 minutes and a standard deviation of σ= 6 minutes. (That is we assume that the delivery process is operating effectively)
1. Describe the shape of the population of all possible sample means. How do you know what the shape is?
2. Find the mean of the population of all possible sample means.
3. Find the standard deviation of the population of all possible sample means
4. Calculate an interval containing 99.73% of all possible sample means.
b. Suppose that the mean of the five sampled delivery times on a particular evening is x¯ = 55 minutes. Using the interval that was calculated in a(4), what would you conclude about whether the restaurant's delivery process is operating effectively? Why?