The times between successive arrivals of vehicles at a toll booth were observed as follows: 4.61, 0.33, 0.51, 3.23, 0.23, and1.79 minutes. (a) Find the sample mean and the sample variance. (b) Find the 1st quartile, median and 3rd quartile. (c) Draw a box-plot of the data. Briefly comment on the possible presence of outliers.
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 times between successive arrivals of vehicles at a toll booth were observed as follows:
4.61, 0.33, 0.51, 3.23, 0.23, and 1.79 minutes.
(a) Find the sample mean and the sample variance.
(b) Find the 1st quartile, median and 3rd quartile.
(c) Draw a box-plot of the data. Briefly comment on the possible presence of outliers.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe0d16b1f-7f5d-4619-adf3-b3b02da14b86%2F1f3edf5b-8f33-4755-a653-4ccf081db719%2Fnge7opb_processed.png&w=3840&q=75)
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