The following histogram displays the distribution of battery life (in hours) for a certain battery model used in cell phones:Suppose that battery life is a normal random variable with μ = 8 and σ = 1.2. Using the standard deviation rule, what is the probability that a randomly chosen battery will last between 6.8 and 9.2 hours? 0.50 0.68 0.95 0.997
Question
The following histogram displays the distribution of battery life (in hours) for a certain battery model used in cell phones:Suppose that battery life is a normal random variable with μ = 8 and σ = 1.2. Using the standard deviation rule, what is the probability that a randomly chosen battery will last between 6.8 and 9.2 hours? 0.50 0.68 0.95 0.997
Solution
To solve this problem, we need to use the standard deviation rule for a normal distribution. This rule states that approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
Given that the mean (μ) is 8 hours and the standard deviation (σ) is 1.2 hours, a battery life of 6.8 hours is 1 standard deviation below the mean and a battery life of 9.2 hours is 1 standard deviation above the mean.
Therefore, the probability that a randomly chosen battery will last between 6.8 and 9.2 hours is approximately 0.68 or 68%, according to the standard deviation rule.
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