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The time until recharge for a battery in a laptop computer under common conditions is normally distributed with a mean of 290 minutes and a standard deviation of 60 minutes. What is the probability of the battery taking more than a certain amount of time to recharge?

User Snookums
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Final answer:

The time until recharge for a battery in a laptop computer follows a normal distribution with a mean of 290 minutes and a standard deviation of 60 minutes. To find the probability of the battery taking more than a certain amount of time to recharge, calculate the z-score and use a standard normal distribution table or calculator.

Step-by-step explanation:

The time until recharge for a battery in a laptop computer follows a normal distribution with a mean of 290 minutes and a standard deviation of 60 minutes.



To find the probability of the battery taking more than a certain amount of time to recharge, we need to convert the problem to a standard normal distribution by using the z-score formula:



z = (x - μ) / σ



Where z is the z-score, x is the specific time for recharging, μ is the mean, and σ is the standard deviation.



Once we calculate the z-score, we can use a standard normal distribution table or a calculator to find the corresponding probability.



Let's say we want to find the probability of the battery taking more than 350 minutes to recharge:




  1. Calculate the z-score:

    z = (350 - 290) / 60 = 1

  2. Look up the probability of z > 1 using a standard normal distribution table or a calculator.

    The probability of z > 1 is approximately 0.1587.



Therefore, the probability of the battery taking more than 350 minutes to recharge is approximately 0.1587, or 15.87%.

User Donmelchior
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