Question

A if two events are mutually exclusive, then their interexction probability will be freater than zero

B For the standard normal probaility distribution, the area to the left of the mean is greater than 0.5

C as the number of degrees of freedom in a t distribution increases, the difference between the T distribution and the standard normal distribution becomes smaller

This 3 statement is true or false

Answer 1

A. False

If two events are mutually exclusive, learning that one of them happened tells us that the other did not happen. The conditional probability of the second event given the first is zero. So, if two events are mutually exclusive, they cannot both occur in the same trial. The probability of their intersection is zero.

B. False

the area to the left of the mean is not greater than 0.5 it is equal to 0.5 in a standard normal probability distribution.

C. True

it is the property of the t distribution that the greater the degree of freedom, the more closely the t distribution resembles the standard normal distribution. As the degree of freedom increases, the area in the tails of the t distribution decreases while the area near the center increases.