Answer :
Around 45.22% of these batteries would be expected to survive beyond 900 days. The z-table may not have the exact value for 1.67, but you can approximate it by using the closest available values and interpolating.
The percentage of automotive batteries that would be expected to survive beyond 900 days can be determined by finding the area under the normal distribution curve. In this case, we know that the mean (μ) is 800 days and the standard deviation (σ) is 60 days.
To find the percentage, we need to calculate the z-score for 900 days. The z-score measures how many standard deviations a value is from the mean.
The formula for calculating the z-score is:
z = (x - μ) / σ
Plugging in the values, we have:
z = (900 - 800) / 60
z = 1.67
Next, we can use a z-table or a calculator to find the percentage of the area to the right of the z-score. The z-table gives us the proportion of the area under the curve.
Looking up the z-score of 1.67 in the z-table, we find that the proportion to the right is approximately 0.4522.
To convert this proportion to a percentage, we multiply it by 100:
0.4522 * 100 = 45.22%
Therefore, we can conclude that approximately 45.22% of the automotive batteries would be expected to survive beyond 900 days.
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