Transcript Advanced Math Topics - San Ramon Valley High School

Advanced Math Topics
6.4 Variation and Standard Deviations of a
Probability Distribution
Suppose a manufacturer states that a tire will last 20,000 miles on average. If a tire
goes out at 12,000 miles, is that reasonable to attribute to chance?
This can be answered by finding the standard deviation of a probability distribution
And seeing how many standard deviation 12,000 is from the mean of 20,000.
Variance:
σ2 = Σ(x – μ)2 • p(x)
Standard deviation:
σ = √variance
σ2 = Σ(x – μ)2 • p(x)
A bowling ball manufacturer makes bowling balls in 2 pound intervals from 8 to 18
pounds. The probability that a customer will buy a particular weighted ball is shown.
Find the mean, variance, and standard deviation.
x (lbs.)
p(x)
x • p(x)
8
0.11
0.88
10
0.21
12
x-μ
(x – μ)2
(x – μ)2 • p(x)
8 – 12.6 = -4.6
21.16
(21.16)(0.11) = 2.33
2.10
10 – 12.6 = -2.6
6.76
(6.76)(0.21) = 1.42
0.28
3.36
12 – 12.6 = -0.6
0.36
(0.36)(0.28) = 0.10
14
0.17
2.38
14 – 12.6 = 1.4
1.96
(1.96)(0.17) = 0.33
16
0.13
2.08
16 – 12.6 = 3.4
11.56
(11.56)(0.13) = 1.50
18
0.10
1.80
18 – 12.6 = 5.4
29.16
(29.16)(0.10) = 2.92
μ = 12.6
σ2 = 8.6
σ = √8.6 ≈ 2.93
From the HW P. 306
3) Janet is a medical lab technician. The number of EEG’s that she takes daily and
the associated probabilities are shown. Find the mean, variance, and standard
deviation for the distribution.
x (EEG’s)
p(x)
0
0.08
1
0.09
2
0.13
3
0.07
4
0.14
5
0.23
6
0.19
7
0.07
μ = 3.9
σ = √4.29 ≈ 2.07
σ2 = 4.29
From the HW P. 306
P. 306 #3-7