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Answer :
The fraction of these batteries that would be expected to survive beyond 1000 days is 0.0021 or approximately 0.21%.
To find the fraction of automotive batteries that would be expected to survive beyond 1000 days, we need to use the information given about the mean and standard deviation of the battery life.
We know that the mean (average) battery life is 900 days, and the standard deviation is 35 days. This means that the distribution of battery life follows a normal curve, with most batteries falling within a range of values centered around the mean.
To find the fraction of batteries that would survive beyond 1000 days, we need to calculate the z-score for this value. The z-score represents the number of standard deviations that a value is from the mean.
The formula for calculating the z-score is:
z = (x - μ) / σ
where x is the value we are interested in (1000 days), μ is the mean (900 days), and σ is the standard deviation (35 days).
Plugging in these values, we get:
z = (1000 - 900) / 35 = 2.86
We can use a z-score table or calculator to find the proportion of values beyond this z-score.
From the z-score table, we can see that the area beyond a z-score of 2.86 is 0.0021. This means that only 0.21% of automotive batteries would be expected to survive beyond 1000 days.
Therefore, the fraction of these batteries that would be expected to survive beyond 1000 days is 0.0021 or approximately 0.21%.
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