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IRISSAK [1]
2 years ago
13

From the information in the graph, what is the mode for the number of books the boys read?

Mathematics
1 answer:
Natalija [7]2 years ago
4 0

Using the graph and the mode concept, it is found that the mode for the number of books the boys read is given by:

  • A. 3

<h3>What is the mode?</h3>
  • The <em>mode </em>of a data-set is the <u>number that appears the most times</u> in it.

In this problem, the data-set is composed by the number of books read by boys each day, and is {7, 2, 3, 5, 3}.

  • The number 3 appears twice on the data-set, which is more times than the other numbers, hence, it is the mode of the data-set, and option A is correct.

You can learn more about the mode concept at brainly.com/question/24732674

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If you round the given number to the nearest thousand, you get 1,703,000. This will then convert to 1.703 \times 10^6 when you convert to scientific notation. The '6' tells us to move the decimal point 6 spots to the right to get 1,703,000 back again.

So this is why the answer is choice B.
8 0
3 years ago
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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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Answer:

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Step-by-step explanation:

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