Question

in a certain normal distribution, 6.3% of the area lies to the left of 36 and 6.3% of the area lies to the right of 42. Find the mean and the standard deviation ?

Answer 1

As the normal distribution is symmetric the mean is (36 + 42) / 2 = 39

p(X < 42) = 1 - 0.063 = 0.937

From tables Φ (1.53) = 0.9370

From this time:

42 is 1.53 standard deviations above the mean

42 = 39 + 1.53s

1.53s = 3

Standard deviation is = 1.96