Fire! An insurance company estimates that it shouldmake an annual profit of $150 on each homeowner’spolicy written, with a standard deviation of $6000.a) Why is the standard deviation so large?b) If it writes only two of these policies, what are themean and standard deviation of the annual profit?c) If it writes 10,000 of these policies, what are the meanand standard deviation of the annual profit?d) Is the company likely to be profitable? Explain.e) What assumptions underlie your analysis? Can youthink of circumstances under which those assumptionsmight be violated? Explain.
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.
Fire! An insurance company estimates that it should
make an annual profit of $150 on each homeowner’s
policy written, with a standard deviation of $6000.
a) Why is the standard deviation so large?
b) If it writes only two of these policies, what are the
mean and standard deviation of the annual profit?
c) If it writes 10,000 of these policies, what are the mean
and standard deviation of the annual profit?
d) Is the company likely to be profitable? Explain.
e) What assumptions underlie your analysis? Can you
think of circumstances under which those assumptions
might be violated? Explain.
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