High School

The life of an automotive battery is normally distributed with a mean of 900 days and a standard deviation of 35 days. What fraction of these batteries would be expected to survive beyond 1000 days?

Answer :

Final answer:

To find the fraction of automotive batteries expected to survive beyond 1000 days, use the standard normal distribution to standardize the value of 1000 days. The fraction of batteries expected to survive beyond 1000 days is approximately 76.21%

Explanation:

To find the fraction of automotive batteries that would be expected to survive beyond 1000 days, we can use the concept of the standard normal distribution. First, standardize the given value of 1000 days using the formula z = (x - mean) / standard deviation, where x is the value we want to standardize, mean is the mean of the distribution, and standard deviation is the standard deviation of the distribution.

Using the given information, the mean is 900 days and the standard deviation is m * s = 4 * 35 = 140 days. Plugging in these values, we get z = (1000 - 900) / 140 = 0.7143. We can then use a standard normal distribution table or calculator to find the corresponding probability. In this case, we find that the probability is approximately 0.7621, or 76.21%.

Learn more about Standard Normal Distribution here:

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