The shelf life of a battery produced by one major company is known to be Normally distributed, with a mean life of 3.5 years and a standard deviation of 0.75 years. What is the upper quartile of battery shelf life? Use the fact that the middle 50% of the data falls within 0.67 standard deviations from the mean.
A) 4.0025 years
B) 4.25 years
C) 4.17 years
D) 5.25 years

Question

Quizplus · Accepted Answer

The upper quartile (Q3) is the point below which 75% of the observations fall. Given that the middle 50% of the data falls within ±0.67 standard deviations from the mean, the upper quartile would be 0.67 standard deviations above the mean. Therefore, Q3 = mean + (0.67 * standard deviation) = 3.5 + (0.67 * 0.75) = 3.5 + 0.5025 = 4.0025 years.

The Shelf Life of a Battery Produced by One Major