Answer:
The probability density function is
f
(
x
)
=
1
b
−
a
for a ≤ x ≤ b.
For this example, X ~ U(0, 23) and
f
(
x
)
=
1
23
−
0
for 0 ≤ X ≤ 23.
Formulas for the theoretical mean and standard deviation are
μ
=
a
+
b
2
and
σ
=
√
(
b
−
a
)
2
12
For this problem, the theoretical mean and standard deviation are
μ
=
0
+
23
2
=
11.50
seconds
and
σ
=
√
(
23
−
0
)
2
12
=
6.64
seconds
