A study was conducted on the average commuting distance of students at Surry Community College. The study found that the first sample of thirty students has an average commute of 23.1 miles with a sample standard deviation of 12.47 miles. The commuting mileages for a second sample of 30 students are below. 20 34 20 20 15 16 19 3 1 15 12 18 15 13 1 12 8 11 20 10 7 13 13 32 7 4 63 18 24 6 A. Find the range, variance and standard deviation for the second sample students.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
A study was conducted on the average commuting distance of students at Surry Community College. The study found that the first sample of thirty students has an average commute of 23.1 miles with a sample standard deviation of 12.47 miles. The commuting mileages for a second sample of 30 students are below.
|
20 |
34 |
20 |
20 |
15 |
16 |
19 |
3 |
1 |
15 |
|
12 |
18 |
15 |
13 |
1 |
12 |
8 |
11 |
20 |
10 |
|
7 |
13 |
13 |
32 |
7 |
4 |
63 |
18 |
24 |
6 |
A. Find the
B. Find the
C. Explain why the average for the second sample is a better representation of the population of students commuting to SCC. Which statistic from above proves this is the better value?
D. Use Chebyshev’s Theorem to find the smallest interval centered on the mean that contains at least 88.9% of the data values for the second sample. Then determine the actual percentage of data contained with the interval.
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