Question 4.20: Refer to Example 4.19. Find the 40th percentile of battery l...

From the z table, the closest area to 0.4000 is 0.4013, corresponding to a z-score of – 0.25. The population of lifetimes has mean 50 and standard deviation 5. The 40th percentile is the point 0.25 standard deviations below the mean. We find this value by converting the z-score to a raw score, using Equation (4.10):

z=\frac{x-\mu}{\sigma}        (4.10)

-0.25=\frac{x-50}{5}

Solving for x yields x = 48.75. The 40th percentile of battery lifetimes is 48.75 hours. See Figure 4.9.