6)- A manufacturing company has developed a fuel-efficient machine that combines pressure washing with steam cleaning. It is designed to deliver 7 gallons of cleaner per minute at 1,000 pounds per square inch for pressure washing. In fact, it delivers an amount at random anywhere between 6.5 and 7.5 gallons per minute. Assume that y, the amount of cleaner delivered, is a uniform random variable with probability density fM) = {% if 6.5 < y < 7.5 elsewhere 1. Find the mean and standard deviation of y. Graph f(y), showing the locations of the mean, 1 and 2 standard deviation intervals around the mean. 2. Find the probability that more than 7.2 gallons of cleaner are dispensed per minute.
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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