Question

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.

Answer 1

Answer:

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 $-1.64$ that corresponds to 5%.

$z=\frac{x-\mu}{\sigma}$

$-1.64=\frac{x-10}{2}$

$-1.64\cdot 2=\frac{x-10}{2}\cdot 2$

$-3.28=x-10$

$x-10=-3.28$

$x-10+10=-3.28+10$                        

$x=6.72$  

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