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kolezko [41]
2 years ago
6

On a test, the mean score for a class of 100 students is 80 and the standard deviation of the scores is 10. The professor who ga

ve the test then realizes that she made a scoring error, which she
corrects by adding 5 points to each student's score. The standard deviation of the students' new scores is?
Advanced Placement (AP)
1 answer:
Juli2301 [7.4K]2 years ago
7 0

Answer:

10

Explanation:

In simple terms, the standard deviation is the average distance of the scores from the mean. If all the scores are increase by the same value (in the case, 5) the average distance from the mean stays the same.

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\bold{\huge{\pink{\underline{ Solution }}}}

<h3><u>Given </u><u>:</u><u>-</u></h3>

  • <u>We </u><u>have </u><u>given </u><u>one </u><u>irregular </u><u>figure </u><u>which </u><u>is </u><u>composed </u><u>2</u><u> </u><u>triangle's </u><u>and </u><u>3</u><u> </u><u>rectangles </u>
  • <u>The </u><u>height </u><u>and </u><u>base </u><u>of </u><u>the </u><u>triangles</u><u> </u><u>is </u><u>6cm </u><u>and </u><u>7</u><u> </u><u>cm</u><u> </u><u>each </u>
  • <u>The </u><u>length </u><u>and </u><u>breath </u><u>of </u><u>the </u><u>rectangles</u><u> </u><u>is </u><u>1</u><u>3</u><u>.</u><u>1</u><u> </u><u>cm </u><u>and </u><u>7cm </u><u>each </u>

<h3><u>To </u><u>Find </u><u>:</u><u>-</u></h3>

  • <u>We </u><u>have </u><u>to </u><u>find </u><u>the </u><u>total </u><u>surface </u><u>area </u><u>of </u><u>the </u><u>given </u><u>figure</u><u>? </u>

<h3><u>Let's </u><u>Begin </u><u>:</u><u>-</u></h3>

<u>We </u><u>have</u><u>, </u>

  • 2 triangles of height 6 cm and base 7cm each
  • 3 rectangles of length 13.1 cm and 7cm each

<u>Therefore</u><u> </u><u>,</u>

<u>We </u><u>know </u><u>that</u><u>, </u>

Area of triangle

\bold{=}{\bold{\pink{\dfrac{1}{2}}}}{\bold{\pink{ × Base × Height }}}

<u>Subsitute </u><u>the </u><u>required </u><u>values</u><u>, </u>

<u>Area </u><u>of </u><u>1</u><u> </u><u>triangle </u>

\sf{=}{\sf{\dfrac{1}{2}}}{\sf{ × 7 × 6 }}

\sf{ = 7 × 3 }

\sf{ = 21 cm²}

<h3><u>Therefore</u><u>, </u></h3>

<u>Area </u><u>of </u><u>2</u><u> </u><u>triangle's </u>

\sf{ = 2 × ( Area\:of\:1\:traingle) }

\sf{ = 2 × 21 }

\sf{ = 42 cm² }

Thus, The area of 2 triangles is 42 cm²

<h3><u>Now</u><u>, </u></h3>

<u>We </u><u>know </u><u>that</u><u>, </u>

Area of rectangle

\bold{\red{ = Length × Breath }}

<u>Subsitute </u><u>the </u><u>required </u><u>values</u><u>, </u>

Area of 1 rectangle

\sf{ = 13.1 × 7 }

\sf{ = 91.7 cm² }

<h3><u>Therefore</u><u>,</u></h3>

<u>Area </u><u>of </u><u>3</u><u> </u><u>rectangles </u>

\sf{ = 3 ×( Area\:of\:1\:rectangle)  }

\sf{ = 3 × 91.7 }

\sf{ = 275.1 cm² }

Thus, The area of 3 rectangle is 275.1 cm²

<h3><u>So</u><u>, </u></h3>

Total area of the given figure

  • = Area of 2 triangles + Area of 3 rectangles

\sf{ = 42 + 275.1 }

\bold{ = 317.1 cm²}

Hence, The total surface area of the given figure is 317.1 cm² .

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