Norfolk, Virginia, a major seaport on the East Coast, has aship coal-loading facility. Currently, coal trucks filled withcoal arrive at the port facility at the mean rate of 149 perday (Poisson distributed). The facility operates 24 hours aday. The coal trucks are unloaded one at a time on a firstcome, first-served basis by automated mechanical equipment that empties the trucks in a constant time of eightminutes per truck, regardless of truck size. The port authority is negotiating with a coal company for an additional30 trucks per day. However, the coal company will not usethis port facility unless the port authority can assure themthat their coal trucks will not have to wait to be unloaded atthe port facility for more than 12 hours per truck on theaverage. Can the port authority provide this assurance?
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.
Norfolk, Virginia, a major seaport on the East Coast, has a
ship coal-loading facility. Currently, coal trucks filled with
coal arrive at the port facility at the mean rate of 149 per
day (Poisson distributed). The facility operates 24 hours a
day. The coal trucks are unloaded one at a time on a firstcome, first-served basis by automated mechanical equipment that empties the trucks in a constant time of eight
minutes per truck, regardless of truck size. The port authority is negotiating with a coal company for an additional
30 trucks per day. However, the coal company will not use
this port facility unless the port authority can assure them
that their coal trucks will not have to wait to be unloaded at
the port facility for more than 12 hours per truck on the
average. Can the port authority provide this assurance?
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