The data in a data set are normally distributed with a mean of 170 and a standard deviation of 20. Estimate the percent of the data that are less than 150 or greater than 190.​

Answers

Answer 1

Using the normal distribution, we find that 32% of the data that is less than 150 or greater than 190.​

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Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

----------------------------

The data in a data set are normally distributed with a mean of 170 and a standard deviation of 20.

This means that [tex]\mu = 170, \sigma = 20[/tex]

----------------------------

Less than 150:

As a proportion, it is the p-value of Z when X = 150, so:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{150 - 170}{20}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a p-value of 0.16.

0.16x100% = 16%

----------------------------

More than 190:

As a proportion, it is 1 subtracted by the p-value of Z when X = 190, so:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{190 - 170}{20}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a p-value of 0.84.

1 - 0.84 = 0.16

0.16x100% = 16%

----------------------------

Estimate the percent of the data that are less than 150 or greater than 190.​

We add both percentages, thus:

16% + 16% = 32%

32% of the data that is less than 150 or greater than 190.​

A similar question is given at https://brainly.com/question/14694610


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Step-by-step explanation:

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Answer:

I dont know

Step-by-step explanation:

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Answer:

the answer is 11, 13, 17

Step-by-step explanation:

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The perimeter of the rectangle is 31 cm.
(b) Work out the width of the rectangle.

Answers

Answer:

Perimeter = 2(L+W)

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31 =18+2W

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5. Find the surface area of a sphere with
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Answers

it should be A) 28.26cm

Select the correct answer.
What is the factored form of this expression?
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Answers

Answer:

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Step-by-step explanation:

since -6 and -6 are factors of 36 that add up to equal -12, the factored form of the expression is (x-6)^2.

at his last baseball game, George missed 35% of the pitches thrown at him. based on this information, how many pitches will he miss if he has 40 pitches thrown at him?

Answers

Answer:

14

Step-by-step explanation:

35% of 40

= 35/100 × 40

= (35×4)/10

= 140/10

= 14

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Answers

Answer:

I dont know I am sorry I really had to ask a question and i don't have enough points so sorry you can report me if you want but I really need some

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ZABD and ZDBC are supplementary angles.
What is the measure of x?
X = [?]°
DR
X 148
B
>C
AT
Angles are not drawn to scale.

Answers

Answer:

Solution given:

x+148=180°[linear pair]

x=180°-148=32°

x=32° is your answer

Answer:

Solution:

Given,

X+48°=180°

X=180°-48°

X=32°

so,

X=32° answer

hope it is helpful to you

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Answers

The correct order of reasons that complete the proof is:

Given

AB = 6 units

BC = 4 units

AC = 4 units

Diagonals are congruent

AC = BD = 4 units

ABCD is a rhombus

ABCD is a square.

Based on the given statements and reasons, let's determine the correct order of reasons to complete the proof that ABCD is a square.

Given: ABCD is a rectangle with vertices A, B, C, and D.

Reason: Given.

AB = 6 units.

Reason: The length of AB is given as 6 units.

BC = 4 units.

Reason: The length of BC is given as 4 units.

AC = 4 units.

Reason: Since ABCD is a rectangle, opposite sides are equal. Therefore, AB = CD = 6 units and BC = AD = 4 units.

Diagonals are congruent.

Reason: In a rectangle, the diagonals are congruent. Therefore, AC = BD.

AC = BD = 4 units.

Reason: From reason 4, we know that AC = 4 units. From reason 5, we know that AC = BD.

ABCD is a rhombus.

Reason: In a rhombus, all sides are equal, and opposite angles are congruent. Since AC = BD = 4 units (reason 6), ABCD satisfies the properties of a rhombus.

ABCD is a square.

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Therefore, the correct order of reasons that complete the proof is:

Given

AB = 6 units

BC = 4 units

AC = 4 units

Diagonals are congruent

AC = BD = 4 units

ABCD is a rhombus

ABCD is a square.

For more questions on square

https://brainly.com/question/27307830

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For which color is the difference between the theorectical probability and experimental probability greatest? A. Brown; The experimental probability is 19.52%, and the theoretical probability is 25%. B. Orange; The experimental probability is 18.9%, and the theoretical probability is 15%. C. Yellow; The experimental probability is 16.96%, and the theoretical probability is 20%. D. Green; The experimental probability is 22.7%, and the theoretical probability is 15%.

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Answer: green

Step-by-step explanation:

find the value of x in the isosceles triangle shown below

Answers

Answer:

[tex]x=6[/tex]

Step-by-step explanation:

[tex]x=\sqrt{52-4^2}=6[/tex]

ANSWER=

X=6


MARK ME BRAINLIEST PLEASE

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Answers

Answer:

24 square units

Step-by-step explanation:

When the sides are doubled, new figure so obtained will have:

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Height (h) = 2*4 = 8 units

Area of the figure when each sides are doubled

[tex] = \frac{1}{2} \times b \times h \\ \\= \frac{1}{2} \times 6 \times 8 \\ \\ = 3 \times 8 \\ \\ = 24 \: square \: unite[/tex]

Math 1 Sem 1 1 2.1.5 Quiz: Naming Functions Question 4 of 6 When you read S(h) aloud, you can shorten it to "S of h." O A. True O B. False​

Answers

Answer: True!

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Please help no links please help no links

Answers

Ok so the first thing you want to do is find the area of the front triangle.

14x10=140

140/2=70

So you have the area of the triangle

Now you just need to times it by 19 to get the depth

70x19=1330

Answer

1330 inches cubed

:)

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Answers

Answer:

4/10, 6/15, 8/20, 10/25

Step-by-step explanation:

HOW LONG IS PQ?
special right triangles khan academy

Answers

Answer:

Step-by-step explanation:

The side opposite to the angle 30 degree in right triangle is half of hypothenuse.

nabiha wants to decorate her home for an upcoming party she bought a roll of ribbon from "dollarama" which is 3.2 m long

(a) how many 15 cm of ribbon can be cut from a 3.2m long ribbon
(b) how long is the remaining peice

Answers

Answer:

A = 21

B = 5

Step-by-step explanation:

1 meter = 100 centimeters

This means that she has 320cm of ribbon. Now you need to divide 320 by 15

320/15 = 21.3333333333

So to check your work you could multiply 15 by 21

15 x 21 = 315

This answer is less than 320 so you now know that Nabiha can cut 21 pieces of ribbon that are 15cm long. You also know that the remaining piece is 320 - 315 = 5.

Please award me brainiest! Hope this helps!

Consider the angle shown below with an initial ray pointing in the 3-o'clock direction that measures θ radians (where 0≤θ<2π). The circle's radius is 2 units long and the terminal point is (−1.15,−1.64).



The terminal point is how many radius lenghts to the right of the circle's center?
h=

Then, cos−1(h)=

Does the number we get in part (b) give us the correct value of θ? 

Therefore, θ=


Answers

Answer:

hello attached below is the sketch of the missing diagram

a) h = 2

b) cos^-1 ( 2 ) = ∞

c ) θ ≈ 215°

Step-by-step explanation:

a) The length ( h ) to the right of the circles center

= h^2 = ( -1.15)^2 + ( -1.64)^2

∴ h = 2

b) cos^-1 ( 2 ) = ∞

c) The value gotten from b does not give us the value of θ

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BC = -1.15

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sin^-1 ( - 1.64 / -1.15 )

cos^1 ( -1.15 / 2 ) gives us the value of θ

tan^-1 ( -1.64 / -1.15 )

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What is the solution set of x2 – 10 = 30x?

{–220, 250}
{–250, 220}
{15 – StartRoot 235 EndRoot, 15 + StartRoot 235 EndRoot}
{–15 – StartRoot 235 EndRoot, –15 + StartRoot 235 EndRoot}

Answers

9514 1404 393

Answer:

  (c)  {15 -√235, 15 +√235}

Step-by-step explanation:

For solutions p and q, the trinomial is ...

  (x -p)(x -q) = x² -(p+q)x +pq

That is, the constant term (-10) must be the product of the roots, and the x-coefficient (-30) must be the opposite of their sum.

The sums of roots in the answer choices are ...

  a) 30

  b) -30

  c) 30

  d) -30

We know the sum of roots is 30, so we can eliminate choices 'b' and 'd'.

The product of the roots must be -10, eliminating choice 'a'. Thus, the only viable choice is C.

_____

The product of the roots of C is ...

  (15 -√235)(15 +√235) = 15² -235 = -10 . . . . as required

Answer:

C

Step-by-step explanation:

what percentage of this shape is shaded?

Answers

Answer:

50%

Step-by-step explanation:

please help i am stuck and trying not to fail lol. also if you can show work pls

Answers

Given:

The figure of rectangle.

To find:

a. The diagonal of the rectangle.

b. The area of the rectangle.

c. perimeter of the rectangle.

Solution:

(a)

In a right angle triangle,

[tex]\sin \theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]

[tex]\sin 30=\dfrac{12}{Hypotenuse}[/tex]

[tex]\dfrac{1}{2}=\dfrac{12}{Hypotenuse}[/tex]

[tex]Hypotenuse=12\times 2[/tex]

[tex]Hypotenuse=24[/tex]

So, the diagonal of the of the rectangle is 24 units.

(b)

In a right angle triangle,

[tex]\tan \theta=\dfrac{Perpendicular}{Base}[/tex]

[tex]\tan 30=\dfrac{12}{Base}[/tex]

[tex]\dfrac{1}{\sqrt{3}}=\dfrac{12}{Base}[/tex]

[tex]Base=12\sqrt{3}[/tex]

Length of the rectangle is 12 and width of the rectangle is [tex]12\sqrt{3}[/tex]. So, the area of the rectangle is:

[tex]Area=length \times width[/tex]

[tex]Area=12 \times 12\sqrt{3}[/tex]

[tex]Area=144\sqrt{3}[/tex]

So, the area of the rectangle is [tex]144\sqrt{3}[/tex] sq. units.

(c)

Perimeter of the rectangle is:

[tex]P=2(length+width)[/tex]

[tex]P=2(12+12\sqrt{3})[/tex]

[tex]P=24+24\sqrt{3}[/tex]

[tex]P\approx 65.57[/tex]

Therefore, the perimeter of the rectangle is about 65.57 units.

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I graphed them

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Answers

Step-by-step explanation:

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Answers

Answer:

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Answers

Answer:

Step-by-step explanation:

Using the comparison, substitution, and elimination method, the answer is:(x,y)=(3,-2)

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