Mathematics, 21.10.2020 16:01, minie66

Travel time data is collected on an arterial. With 30 runs, an average travel time of 152 seconds is computed over the 2.0 miles length, with a computed standard deviation of 17.3 seconds. Required:
a. Compute 95% confidence bounds on your estimate of the mean.
b. Was it necessary to make any assumption about the shape of the travel-time distribution?

Answers: 3

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answered: Leonardo8366

The 95% confidence bounds is $145.80 < \mu < 158.19$

It was not necessary to make any assumption about the shape of the travel time distribution

Step-by-step explanation:

From the question we are told that

The sample size is n = 30

The sample mean is $\=x = 152$

The standard deviation is $\sigma = 17.3 \ second$

From the question we are told the confidence level is 95% , hence the level of significance is

$\alpha = (100 - 95 ) \%$

=> $\alpha = 0.05$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }$

=> $E = 1.96 * \frac{17.3 }{\sqrt{30} }$

=> E = 6.19

Generally 95% confidence bounds is mathematically represented as

$\= x -E < \mu < \=x +E$

=> $152 -6.19 < \mu < 152 -6.19$

=> $145.80 < \mu < 158.19$

This 95% confidence bounds show that there is 95% confidence that the true mean lies within this bound hence there is it was not necessary to make any assumption about the shape of the travel time distribution

answered: Guest

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step-by-step explanation:

answered: Guest

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

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Travel time data is collected on an arterial. With 30 runs, an average travel time of 152 seconds is...