Mean Replacement Times The manager of the Portland Electronics store is concerned that his suppliers have been giving him TV sets with lower than average quality. His research shows that replacement times for TV sets have a mean of 8.2 years and a standard deviation of 1.1 years (based on data from “Getting Things Fixed,” Consumer Reports). He then randomly selects 50 TV sets sold in the past and finds that the mean replacement time of 7.8 years. a) Assuming that TV replacement times have a mean of 8.2 years and a standard deviation of 1.1 years, find the probability that 50 randomly selected TV sets will have a mean replacement time of 7.8 years or less. b) Based on the result from part (a) does it appear that the Portland Electronics store has been given TV sets with lower than average quality?
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.
- a) Assuming that TV replacement times have a mean of 8.2 years and a standard deviation of 1.1 years, find the
probability that 50 randomly selected TV sets will have a mean replacement time of 7.8 years or less. - b) Based on the result from part (a) does it appear that the Portland Electronics store has been given TV sets with lower than average quality?
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