Use the table to answer each question. Note: Round z-scores to the nearest hundredth and then find the required A values using the table. The weights of all the boxes of corn flakes filled by a machine are normally distributed, with a mean weight of 14.5 ounces and a standard deviation of 0.4 ounce. What percent of the boxes will have the following weights? (Round your answers to one decimal place.) (a) weigh less than 14 ounces % (b) weigh between 13.5 ounces and 15.5 ounces %
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 table to answer each question. Note: Round z-scores to the nearest hundredth and then find the required A values using the table.
The weights of all the boxes of corn flakes filled by a machine are
%
(b) weigh between 13.5 ounces and 15.5 ounces
%
Given that,
Mean, mu= 14.5
Standard deviation, sigma= 0.4
Z score= (X-mu)/sigma
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