Answer :
To determine the fraction of automotive batteries that would be expected to survive beyond 1000 days, we need to calculate the probability that a battery's life exceeds 1000 days, given that it follows a normal distribution with a mean of 900 days and a standard deviation of 35 days.
We can use the standard normal distribution (Z-distribution) to calculate this probability. We need to convert the value of 1000 days into a standardized Z-score using the formula:
Z = (X - μ) / σ
where X is the value we want to convert (1000 days in this case), μ is the mean (900 days), and σ is the standard deviation (35 days).
Z = (1000 - 900) / 35 = 2.857
Using a Z-table or a statistical calculator, we can find the area/probability to the right of Z = 2.857. This area represents the fraction of batteries expected to survive beyond 1000 days.
Looking up the Z-score of 2.857 in a standard normal distribution table, we find that the area to the right is approximately 0.00215.
Therefore, the fraction of automotive batteries expected to survive beyond 1000 days is approximately 0.00215 or 0.215%.
Learn more about fraction here:
https://brainly.com/question/78672
#SPJ11
