Answer:
(a) The value of <em>a</em> is 53.35.
(b) The value of <em>a</em> is 38.17.
(c) The value of <em>a</em> is 26.95.
(d) The value of <em>a</em> is 25.63.
(e) The value of <em>a</em> is 12.06.
Step-by-step explanation:
The probability density function of <em>X</em> is:
Here, 22 < X < 55.
(a)
Compute the value of <em>a</em> as follows:
Thus, the value of <em>a</em> is 53.35.
(b)
Compute the value of <em>a</em> as follows:
Thus, the value of <em>a</em> is 38.17.
(c)
Compute the value of <em>a</em> as follows:
Thus, the value of <em>a</em> is 26.95.
(d)
Compute the value of <em>a</em> as follows:
Thus, the value of <em>a</em> is 25.63.
(e)
Compute the value of <em>a</em> as follows:
Thus, the value of <em>a</em> is 12.06.