Use the table to answer the question. Note: Round z-scores to the nearest hundredth and then find the required A values using the table. A biologist found the wingspans of a group of monarch butterflies to be normally distributed with a mean of 55.5 mm and a standard deviation of 2.8 mm. (a) Find the z-score for the following data value. (Round your answer to two decimal places.) 48.4 mmz48.4= What percent of butterflies had a wingspan less than 48.4 mm? (Round your answer to one decimal place.) % (b) Find the z-scores for the following data values. (Round your answers to two decimal places.) 50 mmz50=56 mmz56= What percent of butterflies had a wingspan between 50 mm and 56 mm? (Round your answer to one decimal place.) %
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.
Given that,
Mean, mu = 55.5
Standard deviation, sigma= 2.8
Z score= (X- mu)/sigma
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