Answer:
![z =\frac{33.3- 34}{\frac{5}{\sqrt{54}}}= -1.028](https://tex.z-dn.net/?f=%20z%20%3D%5Cfrac%7B33.3-%2034%7D%7B%5Cfrac%7B5%7D%7B%5Csqrt%7B54%7D%7D%7D%3D%20-1.028)
![z =\frac{34.3- 34}{\frac{5}{\sqrt{54}}}= 0.441](https://tex.z-dn.net/?f=%20z%20%3D%5Cfrac%7B34.3-%2034%7D%7B%5Cfrac%7B5%7D%7B%5Csqrt%7B54%7D%7D%7D%3D%200.441)
An we can use the normal standard table and the following difference and we got this result:
![P(-1.028](https://tex.z-dn.net/?f=%20P%28-1.028%3Cz%3C0.441%29%3D%20P%28z%3C0.441%29%20-P%28z%3C-1.028%29%20%3D%200.670%20-0.152%20%3D0.518)
Step-by-step explanation:
Assuming this statement to complete the problem "with a standard deviation 5 mpg"
We have the following info given:
represent the mean
represent the deviation
We have a sample size of n = 54 and we want to find this probability:
![P(33.3 < \bar X< 34.3)](https://tex.z-dn.net/?f=%20P%2833.3%20%3C%20%5Cbar%20X%3C%2034.3%29)
And for this case since the sample size is large enough >30 we can apply the central limit theorem and then we can use this distribution:
![\bar X \sim N(\mu , \frac{\sigma}{\sqrt{n}})](https://tex.z-dn.net/?f=%5Cbar%20X%20%5Csim%20N%28%5Cmu%20%2C%20%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%29)
And we can use the z score formula given by:
![z=\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}](https://tex.z-dn.net/?f=%20z%3D%5Cfrac%7B%5Cbar%20X%20-%5Cmu%7D%7B%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D)
And replacing we got:
![z =\frac{33.3- 34}{\frac{5}{\sqrt{54}}}= -1.028](https://tex.z-dn.net/?f=%20z%20%3D%5Cfrac%7B33.3-%2034%7D%7B%5Cfrac%7B5%7D%7B%5Csqrt%7B54%7D%7D%7D%3D%20-1.028)
![z =\frac{34.3- 34}{\frac{5}{\sqrt{54}}}= 0.441](https://tex.z-dn.net/?f=%20z%20%3D%5Cfrac%7B34.3-%2034%7D%7B%5Cfrac%7B5%7D%7B%5Csqrt%7B54%7D%7D%7D%3D%200.441)
An we can use the normal standard table and the following difference and we got this result:
![P(-1.028](https://tex.z-dn.net/?f=%20P%28-1.028%3Cz%3C0.441%29%3D%20P%28z%3C0.441%29%20-P%28z%3C-1.028%29%20%3D%200.670%20-0.152%20%3D0.518)
1. 5 in and 1/3 in: Area = 5/3 in^2
2. 5 in and 4/3 in: Area= 20/3 in^2
3. 5/2 in and 4/3 in: Area=10/3 in^2
4. 7/6 in and 6/7 in: Area = 1 in^2
Step-by-step explanation:
<u>1. 5 in and 1/3 in</u>
Here,
![Let\\l=5\\w=\frac{1}{3}\\Area=l*w\\=5*\frac{1}{3}\\=\frac{5}{3}\ in^2](https://tex.z-dn.net/?f=Let%5C%5Cl%3D5%5C%5Cw%3D%5Cfrac%7B1%7D%7B3%7D%5C%5CArea%3Dl%2Aw%5C%5C%3D5%2A%5Cfrac%7B1%7D%7B3%7D%5C%5C%3D%5Cfrac%7B5%7D%7B3%7D%5C%20in%5E2)
<u>2. 5 in and 4/3 in</u>
Here,
![l= 5\ in\\w=\frac{4}{3}\ in\\Area=l*w\\=5*\frac{4}{3}\\=\frac{20}{3}\ in^2](https://tex.z-dn.net/?f=l%3D%205%5C%20in%5C%5Cw%3D%5Cfrac%7B4%7D%7B3%7D%5C%20in%5C%5CArea%3Dl%2Aw%5C%5C%3D5%2A%5Cfrac%7B4%7D%7B3%7D%5C%5C%3D%5Cfrac%7B20%7D%7B3%7D%5C%20in%5E2)
<u>3. 5/2 in and 4/3 in</u>
![let\\l=\frac{5}{2}\\w=\frac{4}{3}\\Area= \frac{5}{2}*\frac{4}{3}\\=\frac{20}{6}=\frac{10}{3}\ in^2](https://tex.z-dn.net/?f=let%5C%5Cl%3D%5Cfrac%7B5%7D%7B2%7D%5C%5Cw%3D%5Cfrac%7B4%7D%7B3%7D%5C%5CArea%3D%20%5Cfrac%7B5%7D%7B2%7D%2A%5Cfrac%7B4%7D%7B3%7D%5C%5C%3D%5Cfrac%7B20%7D%7B6%7D%3D%5Cfrac%7B10%7D%7B3%7D%5C%20in%5E2)
<u>4. 7/6 in and 6/7 in</u>
<u>Let</u>
![l=\frac{6}{7}\\w=\frac{7}{6}\\Area=l*w\\=\frac{6}{7}*\frac{7}{6}\\=1\ in^2](https://tex.z-dn.net/?f=l%3D%5Cfrac%7B6%7D%7B7%7D%5C%5Cw%3D%5Cfrac%7B7%7D%7B6%7D%5C%5CArea%3Dl%2Aw%5C%5C%3D%5Cfrac%7B6%7D%7B7%7D%2A%5Cfrac%7B7%7D%7B6%7D%5C%5C%3D1%5C%20in%5E2)
<u>Hence,</u>
1. 5 in and 1/3 in: Area = 5/3 in^2
2. 5 in and 4/3 in: Area= 20/3 in^2
3. 5/2 in and 4/3 in: Area=10/3 in^2
4. 7/6 in and 6/7 in: Area = 1 in^2
Keywords: Rectangle, Area
Learn more about rectangles at:
#LearnwithBrainly
None
the slope of the suggested lines is either 1 or -1
and none of the equal to the slope of the red line in the graph wichc is 2
Answer:
Step-by-step explanation:
1/2 x because it is always positive and gives half the value of x