Question

The number of lightning strikes on a square kilometer of open ground in a year has a mean of 6 and a standard deviation of 2.4. These values are typical of most of the S. and are normally distributed. The National Lightning Detection Network uses automatic sensors to watch for lightning in a sample of 10 square kilometers. What average number of lightning strikes would represent the lowest 6.5% for the sampling distribution?

Answer 1

From standard normal tables, we have here:
P(Z < -1.514) = 0.065

Therefore the average number of lightning strikes is computed here as:

$= \bar X - z^*\frac{\sigma}{\sqrt{10}} = 6 - \frac{2.4}{\sqrt{10}} = 5.2411$

Therefore 5.2411 is the required average number of lightning strikes here.