The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 54 ounces and a standard deviation of 11 ounces. Use the Standard Deviation Rule, also known as the Empirical Rule. Suggestion: sketch the distribution in order to answer these questions. i&ii) 99.7% of the widget weights lie between and iii) What percentage of the widget weights lie between 43 and 87 ounces? % (answer as a whole number) iv) What percentage of the widget weights lie below 76 ? % (answer as a whole number)
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.
Use the Standard Deviation Rule, also known as the Empirical Rule.
Suggestion: sketch the distribution in order to answer these questions.
iv) What percentage of the widget weights lie below 76 ? % (answer as a whole number)
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