Nicol (see references) lets the pdf of x be defined by f (x) = ⎧⎪⎪⎨ ⎪⎪⎩ x, 0≤ x ≤ 1, c/x3, 1≤ x < [infinity], 0, elsewhere. find (a) the value of c so that f (x) is a pdf. (b) the mean of x (if it exists). (c) the variance of x (if it exists). (d) p(1/2 ≤ x ≤ 2).

The distribution of the amount of money spent by students for textbooks in a semester is approximately normal in shape with a mean of $235 and a standard deviation of $20. according to the standard deviation rule, how much did almost all (99.7%) of the students spend on textbooks in a semester?