1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Degger [83]
1 year ago
9

Location is known to affect the number, of a particular item, sold by an auto parts facility. Two different locations, A and B,

are selected on an experimental basis. Location A was observed for 13 days and location B was observed for 18 days. The number of the particular items sold per day was recorded for each location. On average, location A sold 39 of these items with a sample standard deviation of 8 and location B sold 55 of these items with a sample standard deviation of 2. Select a 90% confidence interval for the difference in the true means of items sold at location A and B
Mathematics
1 answer:
Mama L [17]1 year ago
5 0

We have two samples, A and B, so we need to construct a 2 Samp T Int using this formula:

  • \displaystyle \overline {x}_1 - \overline {x}_2 \ \pm \ t^{*} \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}  }  

In order to use t*, we need to check conditions for using a t-distribution first.

  • Random for both samples -- NOT STATED in the problem ∴ <u><em>proceed with caution</em></u>!
  • Independence for both samples: 130 < all items sold at Location A; 180 < all items sold at Location B -- we can reasonably assume this is true
  • Normality: CLT is not met; <u>n < 30</u> for both locations A and B ∴ <u><em>proceed with caution</em></u>!

<u>Since 2/3 conditions aren't met, we can still proceed with the problem but keep in mind that the results will not be as accurate until more data is collected or more information is given in the problem.</u>

<u>Solve for t*:</u>

<u></u>

We need the <u>tail area </u>first.

  • \displaystyle \frac{1-.9}{2}= .05

Next we need the <u>degree of freedom</u>.

The degree of freedom can be found by subtracting the degree of freedom for A and B.

The general formula is df = n - 1.

  • df for A: 13 - 1 = 12
  • df for B: 18 - 1 = 17
  • df for A - B: |12 - 17| = 5

Use a calculator or a t-table to find the corresponding <u>t-score for df = 5 and tail area = .05</u>.

  • t* = -2.015

Now we can use the formula at the very top to construct a confidence interval for two sample means.

  • \overline {x}_A=39
  • s_A=8
  • n_A=13
  • \overline {x}_B = 55
  • s_B=2
  • n_B=18
  • t^{*}=-2.015

Substitute the variables into the formula: \displaystyle \overline {x}_1 - \overline {x}_2 \ \pm \ t^{*} \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}  }.

  • 39-55 \  \pm \ -2.015 \big{(}\sqrt{\frac{(8)^2}{13} +\frac{(2)^2}{18} } } \ \big{)}

Simplify this expression.

  • -16 \ \pm \ -2.015 (\sqrt{5.1453} \ )
  • -16 \ \pm \ 3.73139

Adding and subtracting 3.73139 to and from -16 gives us a confidence interval of:

  • (-20.5707,-11.4293)

If we want to <u>interpret</u> the confidence interval of (-20.5707, -11.4293), we can say...

<u><em>We are 90% confident that the interval from -20.5707 to -11.4293 holds the true mean of items sold at locations A and B.</em></u>

You might be interested in
Please hurry I need the answer
timama [110]

Answer:

4.12

Step-by-step explanation:

A^2+b^2=c^2 so 8^2+b^2=9^2 so 64+b^2=81 so b^2=17 so b=4.12

7 0
2 years ago
A rectangular prism has a length of 4 cm and a width of 5 cm.The volume of the prism is 200 cu cm .The height is unknown.Explain
Kaylis [27]

Answer:

Well just gonna explain kn the bottom but the answer is 10

Step-by-step explanation:

what you would have to do first is to jusy do 5x4 which is 20 then since you wanna find the volume yoi qould juat do 200 divide by 20 which is 10

3 0
3 years ago
What is 1×1,000+3×10,000+9×1,000+8×100+5×10+2×1
xenn [34]
Use PEMDAS for this problem.
1 x 1000=   + 1000
3 x 10,000= 30,000
---------------------------
                 + 31000
                       9000
---------------------------
                 + 40000
                         800
--------------------------
                    + 40800
                              50
------------------------------
                       + 40850
                                  2
------------------------------
             Answer: 40,852

Hoped this helped.

~Bob Ross ®
5 0
3 years ago
Is this a right triangle?
andrey2020 [161]

Answer:

D ; Yes because the Pythagorean theorem works

Step-by-step explanation:

The measure of all three sidelengths make a right triangle

5 0
3 years ago
It is known that the life of a particular auto transmission follows a normal distribution with mean 72,000 miles and standard de
scoray [572]

Answer:

a) P(X

P(z

b) P(X>65000)=P(\frac{X-\mu}{\sigma}>\frac{65000-\mu}{\sigma})=P(Z>\frac{65000-72000}{12000})=P(z>-0.583)

P(z>-0.583)=1-P(Z

c) P(X>100000)=P(\frac{X-\mu}{\sigma}>\frac{100000-\mu}{\sigma})=P(Z>\frac{100000-72000}{12000})=P(z>2.33)

P(z>2.33)=1-P(Z

Sicne this probability just represent 1% of the data we can consider this value as unusual.

d) z=1.28

And if we solve for a we got

a=72000 +1.28*12000=87360

So the value of height that separates the bottom 90% of data from the top 10% is 87360.  

Step-by-step explanation:

Previous concepts

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".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Part a

Let X the random variable that represent the life of a particular auto transmission of a population, and for this case we know the distribution for X is given by:

X \sim N(72000,12000)  

Where \mu=72000 and \sigma=12000

We are interested on this probability

P(X

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X

And we can find this probability using excel or the normal standard table and we got:

P(z

Part b

P(X>65000)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X>65000)=P(\frac{X-\mu}{\sigma}>\frac{65000-\mu}{\sigma})=P(Z>\frac{65000-72000}{12000})=P(z>-0.583)

And we can find this probability using the complement rule and excel or the normal standard table and we got:

P(z>-0.583)=1-P(Z

Part c

P(X>100000)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X>100000)=P(\frac{X-\mu}{\sigma}>\frac{100000-\mu}{\sigma})=P(Z>\frac{100000-72000}{12000})=P(z>2.33)

And we can find this probability using the complement rule and excel or the normal standard table and we got:

P(z>2.33)=1-P(Z

Sicne this probability just represent 1% of the data we can consider this value as unusual.

Part d

For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.1   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.9 of the area on the left and 0.1 of the area on the right it's z=1.28. On this case P(Z<1.28)=0.9 and P(z>1.28)=0.1

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=1.28

And if we solve for a we got

a=72000 +1.28*12000=87360

So the value of height that separates the bottom 90% of data from the top 10% is 87360.  

5 0
3 years ago
Other questions:
  • Need help Identify three solutions of the graph shown
    9·1 answer
  • How would you solve this: x^2-9x+18
    14·2 answers
  • I need help ASAP!!!
    15·1 answer
  • Factor the expression completely. 28x2 + 20​
    8·1 answer
  • Hello , how to do 6(iii)?
    15·1 answer
  • In Centerville, 45% of the population is female, and 60% of the population commutes to work daily. Of the total Centerville popu
    7·2 answers
  • the cost of an ad is $1 for every 5 words. If Maria wants to spend no more than $15 dollars on her ad, how many words w can she
    8·1 answer
  • Please answer URGENT
    9·1 answer
  • What is the slope for a line that is perpendicular to the line x = -6?
    10·1 answer
  • The number of murders and robberies per 100,000 population for a random selection of states is shown.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!