The average number of miles (in thousands) that a car's tire will function before needing replacement is 71 and the standard deviation is 18. Suppose that 43 randomly selected tires are tested. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of X? X- N( b. What is the distribution of ? a- N( c. If a randomly selected individual tire is tested, find the probability that the number of miles (in thousands) before it will need replacement is between 70.2 and 72.5.
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.
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It is given that mean and standard deviation are 71 and 18, respectively. The sample size is 43.
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