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Arada [10]
2 years ago
14

The graph shows the height of an elevator over a period of time.

Mathematics
1 answer:
natulia [17]2 years ago
6 0

C. Between E and F and between G and H the elevator could be travelling from a higher floor to a lower floor.

<u>We have to justify all the options with respect to the </u><u>graph </u><u>:-</u>

<u>Option A</u> : Between A and B, the elevator would be travelling from a lower floor to a higher floor. Also between C and D, the elevator would be travelling from a lower floor to a slightly higher floor.

So, this option is <u>not correct.</u>

<u>Option B</u> : Between B and C, the elevator wouldn't go higher. And also the same would happen in between D and E.

So, this option is <u>not correct.</u>

<u>Option C</u> : Between E and F, the elevator would be travelling from higher floor to lower and also between G and H.

So, this option is <u>correct</u>.

<u>Option 4</u> : Between F and G, there would not have much changes. So it will be omitted.

So, this option is <u>not correct.</u>

<u />

Learn more about graph here :

brainly.com/question/4025726

#SPJ10

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Step-by-step explanation:

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Step-by-step explanation:

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3 years ago
Jane wants to estimate the proportion of students on her campus who eat cauliflower. After surveying 24 ​students, she finds 2 w
irina1246 [14]

Answer:

A 95​% confidence interval for the proportion of students who eat cauliflower on​ Jane's campus is [0.012, 0.270].

Step-by-step explanation:

We are given that Jane wants to estimate the proportion of students on her campus who eat cauliflower. After surveying 24 ​students, she finds 2 who eat cauliflower.

Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;

                              P.Q.  =  \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }  ~ N(0,1)

where, \hat p = sample proportion of students who eat cauliflower

           n = sample of students

           p = population proportion of students who eat cauliflower

<em>Here for constructing a 95% confidence interval we have used a One-sample z-test for proportions.</em>

<u>So, 95% confidence interval for the population proportion, p is ;</u>

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5% level

                                                   of significance are -1.96 & 1.96}  

P(-1.96 < \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } } < 1.96) = 0.95

P( -1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } < {\hat p-p} < 1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } ) = 0.95

P( \hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } < p < \hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } ) = 0.95

Now, in Agresti and​ Coull's method; the sample size and the sample proportion is calculated as;

n = n + Z^{2}__(\frac{_\alpha}{2})

n = 24 + 1.96^{2} = 27.842

\hat p = \frac{x+\frac{Z^{2}__(\frac{\alpha}{2}_)  }{2} }{n} = \hat p = \frac{2+\frac{1.96^{2}   }{2} }{27.842} = 0.141

<u>95% confidence interval for p</u> = [ \hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } , \hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } ]

 = [ 0.141 -1.96 \times {\sqrt{\frac{0.141(1-0.141)}{27.842} } } , 0.141 +1.96 \times {\sqrt{\frac{0.141(1-0.141)}{27.842} } } ]

 = [0.012, 0.270]

Therefore, a 95​% confidence interval for the proportion of students who eat cauliflower on​ Jane's campus [0.012, 0.270].

The interpretation of the above confidence interval is that we are 95​% confident that the proportion of students who eat cauliflower on​ Jane's campus is between 0.012 and 0.270.

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Second way is to find 37% of each number and then add it
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