Mathematics, 20.12.2019 23:31 mirmir62

An automobile engineer would like to test his newly invented anti-lock braking system. specifically, he would like to calculate the average number of feet it takes the brakes to stop a car going 50 miles per hour. the engineer took a sample of 6 cars and from this sample calculated a mean stopping distance of 15 feet with a standard deviation of 2.28 feet. assuming stopping distances are normally distributed, what is the 80% confidence interval for the population mean?

Answers: 3

Show answers

Answers

Answer from: michealsfamily

The 80% confidence interval is given by (13.622;16.378)

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Assuming the X the random variable that represent the number of feet it takes the brakes to stop a car going 50 miles per hour follows a normal distribution

$X \sim N(\mu, \sigma)$

$\bar X =15$ represent the sample mean

s=2.28 represent the sample deviation

n=6 sample size selected

Confidence =0.8 or 80%

2) Confidence interval

In order to find the critical value is important to mention that we don't know about the population standard deviation, so on this case we need to use the t distribution. Since our interval is at 80% of confidence, our significance level would be given by $\alpha=1-0.80=0.2$ and $\alpha/2 =0.1$ . The degrees of freedom are given by:

df=n-1=6-1=5

We can find the critical values in excel using the following formulas:

"=T.INV(0.1,5)" for $t_{\alpha/2}=-1.48$

"=T.INV(1-0.1,5)" for $t_{1-\alpha/2}=1.48$

The critical value $tc=\pm 1.48$

Now we can calculate the margin of error (m)

The margin of error for the sample mean is given by this formula:

$m=t_c \frac{s}{\sqrt{n}}$

$m=1.48 \frac{2.28}{\sqrt{6}}=1.378$

The interval for the mean is given by this formula:

$\bar X \pm t_{c} \frac{s}{\sqrt{n}}$

And calculating the limits we got:

$15 -1.48 \frac{2.28}{\sqrt{6}}=13.622$

$15 +1.48 \frac{2.28}{\sqrt{6}}=16.378$

The 80% confidence interval is given by (13.622;16.378)

Answer from: Quest

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall is needed to match the record of 40 inches is given by

$40-37.6\\\\=2.4\ inches$

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.

Answer from: Quest

congruent segments

step-by-step explanation:

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 18:50, karen718

Abag contains 4 red, 7 blue and 5 yellow marbles. event a is defined as drawing a yellow marble on the first draw and event b is defined as drawing a blue marble on the second draw. if two marbles are drawn from the bag, one after the other and not replaced, what is p(b|a) expressed in simplest form? a. 7/16 b. 7/15 c. 14/16 d. 14/15

Answers: 1

continue

Mathematics, 21.06.2019 19:30, ashtonsilvers2003

Evaluate the expression for the given value of the variable. ∣-4b-8∣+∣-1-b^2 ∣+2b^3 ; b=-2

Answers: 2

continue

Mathematics, 21.06.2019 22:10, BreadOfTheBear

Use the spider tool located on page 1 of this activity to draw a 12-pointed star for the new logo. (hint: if the spider rotates 360 degrees -- or 720 degrees or 1080 degrees -- she will be facing in the same direction in which she started. when the spider is done drawing, you want her to be facing in the same direction in which she started. she'll be making 12 rotations, all the same size, so each rotation must be some multiple of 360/12 = 30 degrees.) urgently. been stuck on this problem for around 45 minutes now.! it should be easy if you're smart enough

Answers: 3

continue

Mathematics, 22.06.2019 00:30, bella8751

Which graph of a hyperbola represents the equation 16x^2-y^2=16

Answers: 1

continue

You know the right answer?

An automobile engineer would like to test his newly invented anti-lock braking system. specifically,...