Step-by-step explanation:
We will prove by mathematical induction that, for every natural ,
We will prove our base case, when n=4, to be true.
Base case:
Inductive hypothesis:
Given a natural ,
Now, we will assume the induction hypothesis and then use this assumption, involving n, to prove the statement for n + 1.
Inductive step:
With this we have proved our statement to be true for n+1.
In conlusion, for every natural .
Answer:
(A) Mean = 84
(B) Variance = 118.714
(C) Standard deviation = 10.89
Step-by-step explanation:
Data provided:
number of observations, n = 15
sample of 15 costco customer satisfaction scores follow
X
95 11 121
90 6 36
83 -1 1
64 -20 400
95 11 121
98 14 196
80 -4 16
83 -1 1
82 -2 4
93 9 81
86 2 4
80 -4 16
94 10 100
75 -9 81
62 -22 484
================================================
∑X = 1260 ∑= 1662
Now,
(A) Mean =
or
Mean = = 84
(B) Variance =
or
Variance =
or
Variance = 118.714
(C) Standard deviation = √Variance = √118.714 = 10.89