normal distributions 5
1.The final exam scores listed below are from one section of MATH 200. 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 8 out of 20 appliance stores in his neighborhood and asked for the cost of a specific model. Below is the sample data set of prices he collected:
$216 $135 $281 $189 $218 $193 $299 $235
Find the standard deviation.
5.The Company collected a sample of the salaries of its employees. There are 70 salary data points summarized in the frequency distribution below:
Salary |
Number of Employees |
5,001â€“10,000 |
8 |
10,001â€“15,000 |
12 |
15,001â€“20,000 |
20 |
20,001â€“25,000 |
17 |
25,001â€“30,000 |
13 |
- Find the standard deviation.
- Find the variance.
6. Calculate the mean and variance of the sample data set provided below. 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.
- Which number(s) had the highest frequency?
- How many times did a number of 4 or greater get thrown?
- How many times was an odd number thrown?
- 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 sample data below, find the following for each sample:
- Range
- Standard deviation
- 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?