Draw a histogram. How many peaks are there and what they tell us? Whatinference can be made from the mean time interval between the peaks?What is the variance and standard deviation. What is mean by v

1. Traffic Speed.

Draw a histogram. How many peaks are there and what they tell us? What inference can be made from the mean time interval between the peaks? What is the variance and standard deviation. What is mean by variation in this data.

From the given data, let the assumed mean be 63

Mean=

102663+1692p

1081 + 35p

, p= 1

Hence the table becomes,

Standard deviation is given by the formula;

Variance = (34560-63)^2/1116= 16.64

Standard deviation=

Mean by variation for this data is 63

2. 1820, 1590, 1440, 1680, 1730, 1750, 1720, 18pq, 1900

1570, 1700, 1900, 1800, 1770, 2010, 1580, 1620, 1690

1. Write the hypothesis

H0 : μ = 1820
HA : μ > 1820

1. What distribution is to be used? Write reasons

t- tyest distribution is to be used in this hypothesis

1. Calculate the test statistics

Since n= 18, is 1.85 at p-value= 0.189

1. Build the 95% Cl and check the value of the statistics inside the interval if it lies?

1. Construct critical region and draw your conclusion using alpha= 0.05

Since p=0.189 which is greater than alpha 0.05, the hypothesis fails to be rejected.

1. What are implications of making the wrong decision

The implication of making the wrong decision is that the statistic may not fall within the critical region.

3. Plot the given data on a graph paper to get scatter diagram and then determine regression line of y on x. Graph this regression line on the same scatter diagram. Find the sum of the distances from the line to the points. Explain what the method of least square is.

The method of least squares is a standard approach in regression analysis to the approximate solution of overdetermined systems. Least squares means that the overall solution minimizes the sum of the squares of the errors made in the results of every single equation. Least squares problems fall into two categories:

linear or ordinary least squares and non-linear least squares, depending on whether or not the residuals are linear in all unknowns. The linear least-squares problem occurs in statistical regression analysis; it has a closed-form solution. The non-linear problem is usually solved by iterative refinement; at each iteration the system is approximated by a linear one, and thus the core calculation is similar in both cases

4. Evaluate the double integral where D is the region bounded by

i.

=

=

ii.

=

=

iii.

=

=

=

iv.

=

=

=

v. half circle

=

=

5. Construct the vector field F=-pyi +qxj by finding atleast 10 vectors. Find the flux through i.) the square with side b. ii.) a circle with radius p, iii.) a triangle with vertices (-p,o) ,(p,0), (0,q). Find also the curl F.

F(0,0)=0

F(0,1)=Pi , F(1,0)= qj, F(1,2)= qj -2pi, F(0,-1)= pi, F(-1,0)= -qj, F(-1,2)= -2pi-qj, F(2,1)= -pi+2qj, F(-2,1)= -2pi+qj, F(2,0)= 2qj, F(-2,0) = -2qj,

4 y

3

2

1

-4- 3 -2 -1 1 2 3 4 5 x

-1

-2

1. Flux = 4b

2. Flux=

   

3. Flux=

i j

-py qx

Curl of F= 0, meaning that F has a conservative field

6. Evaluate , counterclockwise around the boundary of c the indicated region R: i.)

(

ii.

)

iii.) square with vertices (0,0), (p,0), (p,p), (0,p).

.(p,0, 0,p)=

iv.) Triangle with vertices –p,0, 0,0, 0, p

=

7. Find the volume of a tank whose base dimensions are

i. double integration

v=

=

ii. using triple integrals. Draw also a clear sketch of this tank

y

=\

=dz=

v

z x

8. Find the general solution of the first order differential equation and graph it for atleast 10 values of c using desmos graphing calculator or any other software for graphs.

The integrating factor is given by IF=

=

y= is the general solution.

Applying the condition y(p)= q

Y(p)=