17 18 23 20 26 24 25 34 24 15 28 11 28 20 25 6 8 13 18 13 12 15 23 27 15 32 15 10 24 19 7 7 10 22 25 18 12 23 20 18 9 8 26 27 4 18 10 16 19 11 14 2 20
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.
The paper "Lessons from Pacemaker Implantations" gave the results of a study that followed 89 heart patients who had received electronic pacemakers. The time (in months) to the first electrical malfunction of the pacemaker was summarized in the table below.
| 21 | 14 | 23 | 14 | 4 | 28 | 13 | 17 | 17 | 31 | 4 | 2 |
| 10 | 10 | 26 | 16 | 28 | 16 | 24 | 13 | 22 | 29 | 14 | 29 |
| 21 | 14 | 24 | 24 | 9 | 30 | 29 | 17 | 9 | 26 | 7 | 24 |
| 17 | 18 | 23 | 20 | 26 | 24 | 25 | 34 | 24 | 15 | 28 | 11 |
| 28 | 20 | 25 | 6 | 8 | 13 | 18 | 13 | 12 | 15 | 23 | 27 |
| 15 | 32 | 15 | 10 | 24 | 19 | 7 | 7 | 10 | 22 | 25 | 18 |
| 12 | 23 | 20 | 18 | 9 | 8 | 26 | 27 | 4 | 18 | 10 | 16 |
| 19 | 11 | 14 | 2 | 20 |
| Classes | Frequency | Relative Frequency | Cumulative Relative Frequency |
| 0 - <6 | |||
| 6 - <12 | |||
| 12 - <18 | |||
| 18 - <24 | |||
| 24 - <30 | |||
| 30 - <36 |
(b) Use the cumulative relative frequencies to give approximate answers to the following questions. (Round your answer to four decimal places if needed.)
p =
ii. If the pacemaker must be replaced as soon as the first electrical malfunction occurs, approximately what proportion required replacement between 1 and 2 years after implantation?
p =
(c) Construct a cumulative relative frequency plot. Prepare an Excel document. The file should be named with a .xls extension.
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Use it to answer the following questions. (Round your answers to the nearest whole number if needed.)
t = months
ii. What is the approximate time at which only about 10% of the pacemakers initially implanted were still
t = months
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