The graph shows a Normal distribution The mean of this Normal distribution, to the nearest
tenth, is
1
.
.
3.50 4.00 4.50 5.00 5.50 6.00 6.50

The random variable x has probability density function f (x) = k(−x²+5x−4) 1 ≤ x ≤ 4 or =0 1 show that k = 2/9 find 2 e(x), 3 the mode of x, 4 the cumulative distribution function f(x) for all x. 5 evaluate p(x ≤ 2.5). 6 deduce the value of the median and comment on the shape of the distribution.