Answer the following problems showing your work and explaining (or analyzing) your results.
1. The math grades on the final exam varied greatly. Using the scores below, how many scores were within one standard deviation of the mean? How many scores were within two standard deviations of the mean?
99 34 86 57 73 85 91 93 46 96 88 79 68 85 89
2. The scores for math test #3 were normally distributed. If 15 students had a mean score of 74.8% and a standard deviation of 7.57, how many students scored above an 85%?
3. If you know the standard deviation, how do you find the variance?
4. To get the best deal on a stereo system, Louis called eight appliance stores and asked for the cost of a specific model. The prices he was quoted are listed below:
$216 $135 $281 $189 $218 $193 $299 $235
Find the standard deviation.
5. A company has 70 employees whose salaries are summarized in the frequency distribution below.
Salary Number of Employees
5,001–10,000 8
10,001–15,000 12
15,001–20,000 20
20,001–25,000 17
25,001–30,000 13
a. Find the standard deviation.
b. Find the variance.
6. Calculate the mean and variance of the data. Show and explain your steps. Round to the nearest tenth.
14, 16, 7, 9, 11, 13, 8, 10
7. Create a frequency distribution table for the number of times a number was rolled on a die. (It may be helpful to print or write out all of the numbers so none are excluded.)
3, 5, 1, 6, 1, 2, 2, 6, 3, 4, 5, 1, 1, 3, 4, 2, 1, 6, 5, 3, 4, 2, 1, 3, 2, 4, 6, 5, 3, 1
8. Answer the following questions using the frequency distribution table you created in No. 7.
a. Which number(s) had the highest frequency?
b. How many times did a number of 4 or greater get thrown?
c. How many times was an odd number thrown?
d. How many times did a number greater than or equal to 2 and less than or equal to 5 get thrown?
9. The wait times (in seconds) for fast food service at two burger companies were recorded for quality assurance. Using the data below, find the following for each sample.
a. Range
b. Standard deviation
c. Variance
Lastly, compare the two sets of results.
Company Wait times in seconds
Big Burger Company 105 67 78 120 175 115 120 59
The Cheesy Burger 133 124 200 79 101 147 118 125
10. What does it mean if a graph is normally distributed? What percent of values fall within 1, 2, and 3, standard deviations from the mean?

Continued:

1. Continuing with the data you collected in the Module 1, write a paper (1–3 pages) including all of the following content: • Include your data from Module 1. • Create a frequency distribution table for your data. You can use Excel or Word. • Calculate the standard deviation. • Calculate the variance. • Is this a normal distribution? How do you know? • What are the implications?

Apply any and all resources used to help in this assignment in AP format with website information if applicable.

Referenced from Module 1 Below:
The assignment this week is to collect quantitative data from your daily activities for a minimum of 10 days. Some examples of data to collect are:
• The number of minutes you spend studying every day.
• The time it takes to cook meals each day.
• The amount of daily time spent talking on the phone.
• The amount of time you drive each day.
In a paper (1–3 pages), describe the data you are going to collect and how you are going to keep track of the time. Within the paper, incorporate the concepts we are learning in the module including (but not limited to) probability theory, independent and dependent variables, and theoretical and experimental probability. Discuss your predictions of what you anticipate the data to look like and events that can skew the data. Collect data for at least 10 days. Do you think the data will provide a valid representation of these activities? Explain why or why not.