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.
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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]
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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
Which of the fractions is equivalent to 2/5?
Answer:
4/10, 6/15, 8/20, 10/25
Step-by-step explanation:
two hikers walk on the trans-canada trail for 5.0 h and cover 42km what is there average speed for the trip
Answer:
about 8 km per hour
Step-by-step explanation:
8 kilometers every hour for 5 hours is 40 km wich is very close to 42km. hope this helps
Which numbers between 10 and 20 do not appear in the table at all?
Why don’t they appear?
Answer:
the answer is 11, 13, 17
Step-by-step explanation:
this is because they do not have any even number that multiplies into them.
5. Find the surface area of a sphere with
the radius of 1.5 cm.
a. 28.26 cm
b. 7.065 cm
c. 18.84 cm
d. 14.13 cm
The length of the rectangle is 9 cm.
The perimeter of the rectangle is 31 cm.
(b) Work out the width of the rectangle.
Answer:
Perimeter = 2(L+W)
31 =2(9+w)
31 =18+2W
31-18=2W
13=2W
W=13/2
W=6.5cm
A car is traveling at a speed of y miles per hour. which situation would be described by the expression 1.2y?
Amy buys 22 envelopes for 13p each and pays with a £5 note.
How much change does she get?
Give your answer in pounds, £.
Select the correct answer. Given: is a rectangle with vertices , , , and , where . Prove: is a square. Statements Reasons 1. is a rectangle with vertices , , , and . 1. given 2. units 2. ? 3. units 3. distance formula 4. 4. ? 5. is a square. 5. ? What is the correct order of reasons that complete the proof?
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.
Reason: In a square, all sides are equal, and all angles are right angles. Since ABCD is a rectangle (reason 1) and a rhombus (reason 7), it must also be a square.
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
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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
Answer: True!
Step-by-step explanation: When you pronounce the function you say it as is. :) Please rate and like thank you.
Solve for x 103 (3x+4)
Each side length is doubled. What is the AREA of the new figure?
Answer:
24 square units
Step-by-step explanation:
When the sides are doubled, new figure so obtained will have:
Base (b) = 2*3 = 6 units
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]
Bart owns a neighborhood Kwik-E-Mart. At the end of the day on Wednesday, he counted total receipts in his store of $8,399.70. If the sales tax on food items is 2%, how much merchandise did Bart sell on Wednesday? How much sales tax did he collect?
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?
Answer:
14
Step-by-step explanation:
35% of 40
= 35/100 × 40
= (35×4)/10
= 140/10
= 14
The list below shows the different choices of pizza at the local pizza shop: Pepperoni: 11 Supreme: 7 Cheese: 6 Hawaiian: 3 Based on these results, what is the theoretical probability of choosing a Hawaiian Pizza?
Step-by-step explanation:
11 + 7 + 6 + 3 = 27
total amount of pizza = 27
Hawaiian pizza = 3
3/27 = 1/9
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.
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
what makes 1/3 x > 12 true
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
what percentage of this shape is shaded?
Answer:
50%
Step-by-step explanation:
PLEASE HELP WILL MARK BRAINLIEST
Answer:
Part 1: f(x)=0 has 0 solutions
Part 2: g(x)=0 has 2 solutions
Part 3: h(x)=0 has 1 solution
I graphed them
Select the correct answer.
What is the factored form of this expression?
X^2 - 12x + 36
OA. (x+6)^2
OB. (x - 12)(x - 3)
OC. (x-6)^2
OD. (x-6)(x+6)
Answer:
C
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.
y = –3x + 7
y = 2x – 8
Answer:
Step-by-step explanation:
Using the comparison, substitution, and elimination method, the answer is:(x,y)=(3,-2)
When rewriting the equation the answer is:
3x+y=7
2x-y=8
The scatter plot shows the heights ( in inches) and the shoe sizes of eight men. What is the height of the man whose shoe size is 12?
NO LINKS!!!
Answer: 72 inches
Step-by-step explanation:
please help i am stuck and trying not to fail lol. also if you can show work pls
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.
Which of the following is not an exterior angle of triangle BHE
Answer:
I dont know
Step-by-step explanation:
HOW LONG IS PQ?
special right triangles khan academy
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
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!
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%.
Answer: green
Step-by-step explanation:
find the value of x in the isosceles triangle shown below
Answer:
[tex]x=6[/tex]
Step-by-step explanation:
[tex]x=\sqrt{52-4^2}=6[/tex]
Please help no links please help no links
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=
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
AB = - 1.64
BC = -1.15
AC = 2
sin^-1 ( - 1.64 / -1.15 )
cos^1 ( -1.15 / 2 ) gives us the value of θ
tan^-1 ( -1.64 / -1.15 )
∴ θ ≈ 215°
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}
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: