I just started studying t-distribution on this week. I can't find clear guidance to solve the questions in my lecture note. Can anyone help me out with showing me how to solve the question below? Thank you

b)Calculating quantiles for thet-distribution.

LetT be a random variable which follows a Studentt-distribution with 13degrees of freedom

i) For which number c do we haveP(T

c=

ii) Find the value oft which makes the following statement true:

The middle 95% of the values of T lie betweent andt.

t*=

iii) Find the value oft which makes the following statement true:

The middle 65% of the values of T are in the interval[t , t].

t=