After solving part (a), the city council realizes that it would be too much work to weigh the garbage of that many households. They give up on their hopes of estimating the true mean weight of trash produced within 3 pounds and select a random sample of 15 households and weigh the trash for each of these households on garbage day. Here are the results: 114.8 74.3 80.1 41.5 99.1 31.0 93.1 118.9 26.5 33.1 88.3 46.1 119.7 46.4 19.8 Calculate and interpret a 95% confidence interval for the mean weight of trash for all households in this community.
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.
After solving part (a), the city council realizes that it would be too much work to weigh the garbage of that many households. They give up on their hopes of estimating the true
114.8
74.3
80.1
41.5
99.1
31.0
93.1
118.9
26.5
33.1
88.3
46.1
119.7
46.4
19.8
Calculate and interpret a 95% confidence interval for the mean weight of trash for all households in this community.
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