Briefly discuss the properties of the standard normal ...

[vinney12]

Briefly discuss the properties of the standard normal distribution.

Question 2

Explain why events A and B cannot be mutually exclusive if they are defined on a common sample space with P(A) = 0.56 and P(B) = 0.61.

[brittrenee]

Answer to Question 1

(a) The total area under the normal curve is equal to one.
(b) The distribution is mounded and symmetric with respect to the vertical line drawn through z = 0; it extends indefinitely in directions, approaching but never touching the horizontal axis.
(c) The distribution has a mean of 0 and a standard deviation of 1 .
(d) The mean divides the area in half - 0.50 on each side.
(e) Nearly all the area is between z = -3.00 and z = 3.00

Answer to Question 2

If A and B were mutually exclusive, P(A or B) = 0.56 + 0.61 = 1.17 which is impossible.