Answer:
U
A
S
B
C
Step-by-step explanation:
The sample mean = 11.49 and the sample standard deviation = 6.23.
We will assume that the smiling times, in seconds, follow a uniform distribution between zero and 23 seconds, inclusive. This means that any smiling time from zero to and including 23 seconds is equally likely. The histogram that could be constructed from the sample is an empirical distribution that closely matches the theoretical uniform distribution.
Let X = length, in seconds, of an eight-week-old baby’s smile.
The notation for the uniform distribution is X ~ U(a, b) where a = the lowest value of x and b = the highest value of x.
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
