SOLUTION: 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 deliver

Question 524239: 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  = 45 minutes and a standard deviation of = 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?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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  = 45 minutes and a standard deviation of = 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.
Approximately normal with:
mean of the sample means = 45
std of the sample means = 6/sqrt(5)
----
How do you know what the shape is?
The Central Limit Theorem
--------------------------------------
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.
---
1-0.9973 = 0.0027
(1/2)0.0027 = 0.0014
---
Find the t value with a left tail of 0.0014 when df = 4
t = invT(0.0014,4) = -6.56
Find the correspondiing raw score value using x = ts+u
x = -6.56*2.6833+45 = 27.41
OR x = +6.56*6833+45 = 62.60
Interval with 99.73% of sample means = (27.41,62.60)
-----------------

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?
Seems to be effective. 55 is in the 97% confidence interval.
============
Cheers,
Stan H.
=============

RELATED QUESTIONS
I was wondering if this is right :) 4. When a pizza restaurant�s delivery process is... (answered by stanbon)

hello I have some question and I need the answers today because I have an assignment... (answered by stanbon)

A pizza restaurant manager claims that the average home delivery time for their pizza is (answered by stanbon)

Uncle sal’s pizza plaza has a policy that your pizza will be delivered in 20 minutes or (answered by solver91311)

A local eat-in pizza restaurant wants to investigate the possibility of starting to... (answered by Theo)

I am trying to answer this question from openupresources.org. A restaurant offers... (answered by Alan3354)

I am trying to answer this practice problem from openupresources.org A restaurant... (answered by Alan3354)

There is a 90% chance that a pizza place will make a delivery in less than 30 min. what... (answered by stanbon)

A pizza shop owner determines the number of pizzas that are delivered each day. Find... (answered by Boreal)