ne way to identify penguin colonies is to examine thermal (surface temperature) maps of an area. Penguins appear warmer than their background (remember penguins are mammals). Suppose that on Torgersen Island, thermal values for a colony of penguins are uniformly distributed with a maximum thermal value of 18^{\circ}C18∘C. It has been reported that 20% of colonies report a thermal value of at least 15^{\circ}C15∘C. Based on this information, determine the minimum thermal value for colonies on Torgersen Island.
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.
One way to identify penguin colonies is to examine thermal (surface temperature) maps of an area. Penguins appear warmer than their background (remember penguins are mammals). Suppose that on Torgersen Island, thermal values for a colony of penguins are uniformly distributed with a maximum thermal value of 18^{\circ}C18∘C.
It has been reported that 20% of colonies report a thermal value of at least 15^{\circ}C15∘C.
Based on this information, determine the minimum thermal value for colonies on Torgersen Island.
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