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A consumer advocacy group tested the "on-air" lifetimes a random sample of 241 cell phone batteries. The mean lifetime was 3.2 hours with a standard deviation of 0.1 hours. The lifetimes are approximately bell-shaped. Estimate the number of batteries with lifetimes between 3.0 hours and 3.4 hours. Round your answer to the nearest whole number.

Respuesta :

Using the Empirical Rule, it is found that 229 batteries have lifetimes between 3.0 hours and 3.4 hours.

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By the Empirical Rule, in a normal variable: 68% of the measures are within 1 standard deviation of the mean, 95% are within 2 and 99.7% are within 3.

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  • Mean of 3.2 hours with a standard deviation of 0.2 hours.

3 = 3.2 - 2(0.1)

3.4 = 3.2 + 2(0.1)

  • Thus, between 3 and 3.4 hours is within 2 standard deviations of the mean, which is 95%.
  • Out of 241 batteries: [tex]0.95(241) = 229[/tex]

229 batteries have lifetimes between 3.0 hours and 3.4 hours.

A similar problem is given at https://brainly.com/question/24552083

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