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Artist 52 [7]
3 years ago
9

A set of data following a normal distribution has a mean of 192.3 and a standard deviation of 11.8. Find the probability that a

randomly selected value is less than 212.5
Mathematics
2 answers:
zavuch27 [327]3 years ago
8 0

Answer: 1. B) 0.0611

2. B) 2.79

3. C) 433.5 and 457.4

4. D) 11.25 and 11.81

5. A) 0.6772

6. C) 0.1379

7. C) 137.8

8. D) 0.9564

9. B) 20 and 25

10. D) 20.29

Step-by-step explanation: 100% for stats quiz (please be aware that not all stats quizzes look the same!)

stiks02 [169]3 years ago
7 0
Answer: 95.64% of the values will be below 212.5 in our set of data.

First, determine the z-score for the expected value of 212.5. The z-score is the number of standard deviations that it is above or below the mean.

(212.5 - 192.3) / 11.8 = 1.71

A score of 212.5 is 1.71 standard deviations above the mean. Now, use a table to find the probability for a z-score of 1.71. The percent is 95.64%.
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Instructions:Select the correct answer from each drop-down menu. ∆ABC has vertices at A(11, 6), B(5, 6), and C(5, 17). ∆XYZ has
Akimi4 [234]

to compare the triangles, first we will determine the distances of each side

<span>Distance = ((x2-x1)^2+(y2-y1)^2)^0.5
</span>Solving 

<span>∆ABC  A(11, 6), B(5, 6), and C(5, 17)</span>

<span>AB = 6 units   BC = 11 units AC = 12.53 units
</span><span>∆XYZ  X(-10, 5), Y(-12, -2), and Z(-4, 15)
</span><span>XY = 7.14 units   YZ = 18.79 units XZ = 11.66 units</span>

<span>∆MNO  M(-9, -4), N(-3, -4), and O(-3, -15).</span>

<span>MN = 6 units   NO = 11 units MO = 12.53 units
</span><span>∆JKL  J(17, -2), K(12, -2), and L(12, 7).
</span><span>JK = 5 units   KL = 9 units JL = 10.30 units
</span><span>∆PQR  P(12, 3), Q(12, -2), and R(3, -2)
</span><span>PQ = 5 units   QR = 9 units PR = 10.30 units</span> 
Therefore
<span>we have the <span>∆ABC   and the </span><span>∆MNO  </span><span> 
with all three sides equal</span> ---------> are congruent  
</span><span>we have the <span>∆JKL  </span>and the <span>∆PQR 
</span>with all three sides equal ---------> are congruent  </span>

 let's check

 Two plane figures are congruent if and only if one can be obtained from the other by a sequence of rigid motions (that is, by a sequence of reflections, translations, and/or rotations).

 1)     If ∆MNO   ---- by a sequence of reflections and translation --- It can be obtained ------->∆ABC 

<span> then </span>∆MNO<span> ≅</span> <span>∆ABC  </span> 

 a)      Reflexion (x axis)

The coordinate notation for the Reflexion is (x,y)---- >(x,-y)

<span>∆MNO  M(-9, -4), N(-3, -4), and O(-3, -15).</span>

<span>M(-9, -4)----------------->  M1(-9,4)</span>

N(-3, -4)------------------ > N1(-3,4)

O(-3,-15)----------------- > O1(-3,15)

 b)      Reflexion (y axis)

The coordinate notation for the Reflexion is (x,y)---- >(-x,y)

<span>∆M1N1O1  M1(-9, 4), N1(-3, 4), and O1(-3, 15).</span>

<span>M1(-9, -4)----------------->  M2(9,4)</span>

N1(-3, -4)------------------ > N2(3,4)

O1(-3,-15)----------------- > O2(3,15)

 c)   Translation

The coordinate notation for the Translation is (x,y)---- >(x+2,y+2)

<span>∆M2N2O2  M2(9,4), N2(3,4), and O2(3, 15).</span>

<span>M2(9, 4)----------------->  M3(11,6)=A</span>

N2(3,4)------------------ > N3(5,6)=B

O2(3,15)----------------- > O3(5,17)=C

<span>∆ABC  A(11, 6), B(5, 6), and C(5, 17)</span>

 ∆MNO  reflection------- >  ∆M1N1O1  reflection---- > ∆M2N2O2  translation -- --> ∆M3N3O3 

 The ∆M3N3O3=∆ABC 

<span>Therefore ∆MNO ≅ <span>∆ABC   - > </span>check list</span>

 2)     If ∆JKL  -- by a sequence of rotation and translation--- It can be obtained ----->∆PQR 

<span> then </span>∆JKL ≅ <span>∆PQR  </span> 

 d)     Rotation 90 degree anticlockwise

The coordinate notation for the Rotation is (x,y)---- >(-y, x)

<span>∆JKL  J(17, -2), K(12, -2), and L(12, 7).</span>

<span>J(17, -2)----------------->  J1(2,17)</span>

K(12, -2)------------------ > K1(2,12)

L(12,7)----------------- > L1(-7,12)

 e)      translation

The coordinate notation for the translation is (x,y)---- >(x+10,y-14)

<span>∆J1K1L1  J1(2, 17), K1(2, 12), and L1(-7, 12).</span>

<span>J1(2, 17)----------------->  J2(12,3)=P</span>

K1(2, 12)------------------ > K2(12,-2)=Q

L1(-7, 12)----------------- > L2(3,-2)=R

 ∆PQR  P(12, 3), Q(12, -2), and R(3, -2)

 ∆JKL  rotation------- >  ∆J1K1L1  translation -- --> ∆J2K2L2=∆PQR 

<span>Therefore ∆JKL ≅ <span>∆PQR   - > </span><span>check list</span></span>
6 0
3 years ago
What is 5 multiplied by 3 1/3
maksim [4K]

Answer:

16 2/3 or 16.66 repeating

6 0
3 years ago
6.<br> 5. ¿Qué número tiene el mismo<br> valor que l centena, 7 decenas?
pashok25 [27]

Answer:

7 Decenas = 70 Unidades espero que te ayude

Step-by-step explanation:

5 0
3 years ago
Please help me out? thank you!!!
NeX [460]

Step-by-step explanation:

What you need to do is convert the quarts into gallons and then you need to subtract the number by 2 and you have your answer. Sorry I cannot give you the answer! I'm kinda in a rush but I wanted to help you out.

8 0
3 years ago
Read 2 more answers
Determine the unknown angle measures, to the nearest degree, in the diagram provided.
serg [7]

Answer:

a is <u>5</u><u>3</u><u>.</u><u>8</u><u>°</u><u>,</u> and b is <u>3</u><u>6</u><u>.</u><u>2</u><u>°</u>

Step-by-step explanation:

Using sine trig rule:

{ \boxed{ \bf{ \sin(b) =  \frac{opposite}{hypotenuse}  }}}

{ \tt{ \sin(b) =  \frac{78}{132}  }} \\  \\ { \tt{b =  { \sin }^{ - 1}( \frac{78}{132} ) }} \\  \\ { \tt{b = 36.2 \degree}}

Summation of angles of triangle:

{ \tt{a + b + 90 \degree = 180 \degree}} \\ { \tt{a + 36.2 \degree + 90 \degree = 180 \degree}} \\ { \tt{a = (180 - 36.2 - 90) \degree}} \\ { \tt{a = 53.8 \degree}}

7 0
2 years ago
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