Simpson's Rule
Volume of Revolution
Samples
Intervals & Margins
Sample Sizes
100
Approximate area using Simpson’s Rule with
n=4 from 0 to 4 for :
y=x^2
=64/3 ≈21.33
100
Find the volume from 0 to 1 for
y=x^2
V=π∫x^4 dx=5π, 0->1
100
For the data set 2, 4, 6, 8, 10, find the mean
Mean = 6
100
Compute the 95% confidence interval for the
Sample mean = 50,
Standard Deviation = 10,
and sample size = 25
50±1.96(10/5)=50±3.92 → (46.08, 53.92)
100
Find the required sample size (n) for margin of error 2, with standard deviation of 10, and 95% confidence.
n=(1.96×10/2)^2=96.04→97
200
Approximate using the Simpson's rule
∫(x^3) dx within bounds 0 to 3
≈ 20.25
200
Approximate the volume for
y= sin (x) , 0->pi
200
Compute sample variance for : 5, 7, 9, 11, 13
Variance = 8
200
Compare the confidence interval width when sample size increases from 25 to 100
Larger sample → narrower CI
200
Find (n) for margin of error 6, SD - 20 and 90% confidence.
n=(1.645×20/5)^2≈43
300
BONUS
DOUBLE POINTS
300
Use a calculator to evaluate the volume between 0 to 3
y=2x+1
= 57 pi
300
Find expected value of {1, 2, 3, 4} with probabilities of {0.1, 0.2, 0.3, 0.4}
E(X) = 3.0
300
Calculate the margin of error for a 90% Confidence with mean = 100, SD = 15, Sample population = 36
100±1.645(15/6)=100±4.11
300
Determine the sample size for 95%, SD = 12 and
Margin of error = 3
n=62