A battery has a normally distributed lifetime of 10 years with a standard deviation of 2 years. Find a lower specification limit so that only 5% of batteries that are shipped to market have less than this lifetime.

6.72

Step-by-step explanation:

We have been given that a battery has a normally distributed lifetime of 10 years with a standard deviation of 2 years. We are asked to find a lower specification limit so that only 5% of batteries that are shipped to market have less than this lifetime.

To solve this problem, we need to find z-score corresponding to 5% and then use z-score formula to find sample score.

From normal distribution table, we will get a z-score of that corresponds to 5%.

Therefore, the lower specification limit of batteries would be 6.72.

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