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 is the probability that the average number of lightning strikes in this sample area exceeds 4.4?

Answer 1

Data given:
Mean = 6, SD/root(N) = 0.7589467, P(Y > 4.4) = ?;

P(Y > 4.4) = P(Y - mean > 4.4 - mean)
                  = P( (Y - mean)/(SD/root(N)) > (4.4 - mean)/(SD/root(N))
                  = P(Z > (4.4 - mean)/(SD/root(N)))
                  = P(Z > (4.4 - 6)/0.7589467)
                  = P(Z > -2.108)
                  = 1 - P(Z <= -2.108)
                  = 0.983----------------from normal table.