Question

If a variable can be assumed to be normally distributed, with sample mean of 12.34 and best estimate of the standard deviation of 3.44, what percentage of all sample observations can be expected to have values in the range 8.90 to 15.78?

		34
		95
		68
		5

Answer 1

We let the variable be 'X'

To find the percentage we need to calculate the probabilities within the range 8.90 to 15.78

Then using the normal probability tables we calculate the probabilities.

P(8.90 < X < 15.78) = P( X < 15.78) - P( X < 8.90)

=

= P(Z < 1) - P(Z <-1)

= P(Z <1) - [1 - P(Z < 1)]

= 2P(Z< 1) -1

= 2 * 0.8413 - 1

= 0.683

=