The life of cell batteries is normally distributed with a mean of 92.3 hours and a standard deviation of 23.5 hours. What is the maximum time (in hours) that the worst 13% of batteries last? (2 dec pl )
Question
The life of cell batteries is normally distributed with a mean of 92.3 hours and a standard deviation of 23.5 hours. What is the maximum time (in hours) that the worst 13% of batteries last? (2 dec pl )
Solution
To find the maximum time that the worst 13% of batteries last, we need to find the z-score that corresponds to the 13th percentile in a standard normal distribution.
We can look up this value in a standard normal distribution table or use a calculator with a normal distribution function. The z-score that corresponds to the 13th percentile is approximately -1.13.
We then use this z-score to find the corresponding value in the distribution of battery life times. We use the formula:
X = μ + Zσ
where X is the value we are interested in, μ is the mean (92.3 hours), Z is the z-score (-1.13), and σ is the standard deviation (23.5 hours).
X = 92.3 + (-1.13)(23.5) = 66.05 hours
So, the maximum time that the worst 13% of batteries last is approximately 66.05 hours.
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