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:
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- Calculate the z-score:
z = (350 - 290) / 60 = 1
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- 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%.