MATH MATH E-102 Sets, Counting, and Probability - Harvard University _ Scenario: Battery Life

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Scenario: Battery Life

Instructions: View the video found on page 1 of this journal activity.

Using the information provided in the video, answer the questions below.

Show your work for all calculations The Journal is worth 20 points total.

1. Based on the info from the presentation:

Which company do you think makes the longest-lasting (and better) cell phone? Explain your thinking. (​1 point​​)

Talkalot. Because the battery life is a deviation to 17 hours whereas chatlog comes to 16 hours.

2. Complete the table to summarize each student’s point of view: (​2 points​​, 1 point for each) He believes chatlongs has a longer battery life because of a 18 hour length. But talkalot has a higher deviation.

Student 1

Student 2

Talkalot lasts longer because the average time is longer than chatlongs by 2 hours. The student agrees to try out both phones to test and see which one is better.

3. a. Pick one of the two companies and sketch out a normal curve for it. Be sure to label it and use vertical lines to locate the mean and 1 standard deviation on either side of the mean. (​2 points​​)

Talkalot 20 hours is the average- 3 hours deviation

b. What is the range of values for each company to be within 1 standard deviation? (​2 points​​) Chatlong 16-20 hours Talkalot 17 to 23 hours

c. What is the range for the 68-95-99.7 distribution? (​4 points​​) There is a 68% chance of being with one standard deviation of the mean, 95% chance of being within 2 standard deviations from the mean and there is a 99.7% chance of being within three standard deviations from the mean.

For chatlong, you have a 68% chance of being in the range 16-20 hours, 95% chance of being in the range 14-22 hours, and 99.7% chance of being in the range 12-24 hours.

For talk a lot you have a 68% chance of being in the range 17-23 hours, 95% chance of being in the range 14-26 hours, and 99.7% chance of being in the range 11-29 hours.

d. It may not make sense for the company’s data to be represented by a normal distribution.

Look at the three graphs below represented by a curve and the ​x​-axis. Which one is not possible? Why? (​1 point​​)

4.

The students each buy one cell phone and perform their own experiments to wear out the batteries.

Here are the data:

a. Based on their sample data, which of the cell phones is better? (​1 point​​) The sample data shows that both are the same and does not indicate that either is better but both are the same. b. In order to properly compare the data, calculate the z-scores for each sample data point. (​2 points​​) Chatlong z= (20-18)/2 z=2/2 z=1 Talk a lot z=(20-20)/3 z=0/3 z=0 c. Use a statistical calculator or a standard normal chart to find the percentile for each z-score you found in part b above. (​2 points​​) Two sided chatlong 68.2689 Twosided talkalot 0

d. Now who do you think got the better cell phone (with longer battery life) and why? (​1 point​​) Because of a score of 0, which means it is exact to the mean and having a mean with a deviation of 3 hrs from 20hrs, talkalot is the better cellphone

5. a. Is it problematic to decide that one company is better than another based solely on the students' sample data? Explain. (​1 point​​) Yes it is because not all tech works the same. There is always a margin for error and a detailed experiment would be better than just 2 phones b. How would you improve the students’ experiment if you were going to conduct it yourself? (​1 point​​) I would use at least 5 phones from each provider with 5 test subjects using their phones and documenting the usage. I would use the data to see the same calculations and compared to the student data collected from the first trial.