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kotegsom [21]
3 years ago
12

A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than ex

amine the records for all​ students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. The​ 95% confidence interval for is 0.590.07. Interpret this interval. A. It can be said that​ 95% of the students get between​ 52% and​ 66% of their tuition paid for by financial aid. B. One can be​ 95% confident that between​ 52% and​ 66% of the sampled students receive some sort of financial aid. C. One can be​ 95% confident that the true proportion of all students receiving financial aid is between 0.52 and 0.66. D. One can be​ 95% confident that​ 59% of the students are on some sort of financial aid.
Mathematics
1 answer:
vredina [299]3 years ago
3 0

Answer:

C. One can be​ 95% confident that the true proportion of all students receiving financial aid is between 0.52 and 0.66

Step-by-step explanation:

Given that the confidence interval is a term that defines a range of values with the probability to contain a population value that has an actual degree of confidence.

This is represented in a situation where population means falls in between upper and lower intervals.

Hence, in this case, the correct interpretation is option C: One can be​ 95% confident that the true proportion of all students receiving financial aid is between 0.52 and 0.66

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Vsevolod [243]

Answer:

  • CDs — $10,000
  • bonds — $80,000
  • stocks — $45,000

Step-by-step explanation:

Let the variables c, b, s represent the dollar amounts invested in CDs, stocks, and bonds, respectively. Then the problem statement gives us 3 relations between these 3 variables:

  c + b + s = 135000 . . . . . . . . . . . . . . . . . total invested

  0.0275c +.045b +0.104s = 8555 . . . . . total income earned

  -c + b = 70000 . . . . . . . . . . . . . . . . . . . . . 70,000 more was in bonds than CDs

Using the third equation to write an expression for b, we can substitute into the other two equations.

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  c + (70000 +c) +s = 135000 . . . . substitute for b in the first equation

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  .0725c +.104s = 5405 . . . . . . . . . . [eq5] simplify

Using [eq4], we can write an expression for s that can be substituted into [eq5].

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  0.0725c +0.104(65000 -2c) = 5405

  -0.1355c = -1355 . . . . . . . . . . . . . . . . . . . . subtract 6760, simplify

  c = 1355/.1355 = 10,000

  s = 65000 -2×10000 = 45,000

  b = 70000 +10000 = 80,000

The amounts invested in stocks, bonds, and CDs were $45,000, $80,000, and $10,000, respectively.

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Alternatively, you can reduce the augmented matrix for this problem to row-echelon form using any of several calculators or on-line sites. That matrix is ...

\left[\begin{array}{ccc|c}1&1&1&135000\\0.0275&0.045&0.104&8555\\-1&1&0&70000\end{array}\right]

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Answer:

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I graphed the equation on the graph below to show you how I got my answer.

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y = (1/x) + b. To find b, you plugin the coordinates of either A or B,
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