In a test of a lifelong brand of tires, a survey revealed that the mean life was 35,000 miles and the standard deviation was 7,083 miles. If the shape of the population distribution is known to be normal, approximately what percentage of the tires lasts less than 20,834 miles?
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.
I. In a test of a lifelong brand of tires, a survey revealed that the mean life was 35,000 miles and the standard deviation was 7,083 miles. If the shape of the population distribution is known to be normal, approximately what percentage of the tires lasts less than 20,834 miles?
Solution:
1.
Let X be the lifelong brand of tires.
From the given information, X follows normal distribution with mean µ=35,000 miles and a standard deviation σ=7,083 miles.
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