A factory makes bottles in three colors: 85% of bottles are clear, 10% are green, and 5% are brown. The machine which makes the clear bottles create defects 1.5% of the time. The machine which makes the green bottles create defects 2% of the time. The machine which makes the brown bottles create defects 3% of the time. (a.) What is the probability that a randomly selected bottle is defective? (b.) Given that a randomly selected bottle is defective, what is the probability that it is brown?
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 factory makes bottles in three colors: 85% of bottles are clear, 10% are green, and 5% are brown. The machine which makes the clear bottles create defects 1.5% of the time. The machine which makes the green bottles create defects 2% of the time. The machine which makes the brown bottles create defects 3% of the time.
(a.) What is the
(b.) Given that a randomly selected bottle is defective, what is the probability that it is brown?
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