Identify each of the following statements as either TRUE or FALSE.

a)If T is a random variable with a t distribution, then P(T < 0) = 0.5.

b)The t distribution tends toward the standard normal distribution as the degrees of freedom increase.

c)If we wish to carry out inference procedures on the mean of a normally distributed population where sigma is known, we should use the t distribution.

d)The t distribution has more area in the tails than the standard normal distribution.

e)The t distribution has a standard deviation of 1.