Probability

A fast food restaurant is investigating its processes for ensuring they can meet customer demand for coffee. It is studying the temperature of coffee being dispensed at one of its locations. A temperature measurement is taken at a randomly selected time during each of the 24 half hour periods from 8:00am to 7:30pm on a given day. This is then repeated on the second day so that there are 48 different coffee temperatures. The data set link appears on the right side of the page. You are the manager and you have been asked to perform the analyses to help determine whether temperature control and ordering processes are acceptable or not.

You conduct the following analyses in order to determine whether processes are adequate or not.

1. Create a relative frequency distribution and a histogram based on the coffee temperatures. Classes should consist of 5 degrees (e.g. your first class would be temperatures from 145 to 149 degrees, the second would be 150-154 degrees, etc.)

2. By just looking at the histogram, can you conclude whether the data is normally distributed? What is the basis for your conclusion?

3. Calculate the mean and standard deviation for the temperature data. Find the z value and the accompanying probability for the following observed values of x. In each case, explain what the z value tells us about how the observed value of x compares to the mean.

• x = 144
• x = 156
• x = 164
• x = 171

4. We know that the ideal temperature to maximize the flavor of the coffee is between 155 and 167 degrees. What percentage of the coffee served falls within the range?

5. Based on this, should your management consider changing processes to ensure that the coffee is served at the correct temperatures?

6. If the data were not normally distributed, could you apply the Central Limit Theorem? Explain what the CLT is and how it might help you determine

7. Coffee is made using a process that relies on special filter packs of ground coffee beans. Weekly demand at the restaurant for coffee is normally distributed with a mean of 800 filter packs and a standard deviation of 75 filter packs. What is the probability that the weekly demand is

• 959 filter packs or less?
• More than 1004 filter packs?
• Between 650 filter packs and 950 filter packs?

Data Needed:

Temperature of coffee during 30 minute interval
157
157
149
168
162
170
151
158
165
160
156
162
163
176
169
160
167
161
155
164
176
152
154
165
174
161
158
171
163
153
168
156
168
167
164
157
159
163
163
154
161
165
164
172
162
160
166
169
146
164