Using the normal distribution, it is found that:
a) 4.46% of finish times was higher than 72 minutes.
b) 55.11% of finish times was between 52 and 70 minutes.
c) The 40th percentile of finish times is 52.5 minutes.
d) The 95th percentile of finish times is 71.45 minutes.
In a normal distribution 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]
It 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, which is the percentile of X.In this problem:
The mean is of 55 minutes, hence [tex]\mu = 55[/tex].The standard deviation is of 10 minutes, hence [tex]\sigma = 10[/tex]Item a:
The proportion is 1 subtracted by the p-value of Z when X = 72, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{72 - 55}{10}[/tex]
[tex]Z = 1.7[/tex]
[tex]Z = 1.7[/tex] has a p-value of 0.9554
1 - 0.9554 = 0.0446
0.0446 x 100% = 4.46%
4.46% of finish times was higher than 72 minutes.
Item b:
Th proportion is the p-value of Z when X = 70 subtracted by the p-value of Z when X = 52, hence:
X = 70:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{70 - 55}{10}[/tex]
[tex]Z = 1.5[/tex]
[tex]Z = 1.5[/tex] has a p-value of 0.9332.
X = 52:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{52 - 55}{10}[/tex]
[tex]Z = -0.3[/tex]
[tex]Z = -0.3[/tex] has a p-value of 0.3821.
0.9332 - 0.3821 = 0.5511
0.5511 x 100% = 55.11%
55.11% of finish times was between 52 and 70 minutes.
Item c:
The 40th percentile is X when Z has a p-value of 0.4, so X when Z = -0.253.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.253 = \frac{X - 55}{10}[/tex]
[tex]X - 55 = -0.253(10)[/tex]
[tex]X = 52.5[/tex]
The 40th percentile of finish times is 52.5 minutes.
Item d:
The 95th percentile is X when Z has a p-value of 0.95, so X when Z = 1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 55}{10}[/tex]
[tex]X - 55 = 1.645(10)[/tex]
[tex]X = 71.45[/tex]
The 95th percentile of finish times is 71.45 minutes.
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Write the expression that represents the sum of
double a number and triple a number.
Answer: let x = the "number"
2x + 3x is the expression
Step-by-step explanation:
Ana is a dedicated Skee Ball player (see
photo) who always rolls for the 50-point slot. The
probability distribution of Ana’s score X on a single
roll of the ball is shown below. You can check that
Mx = 23.8 and og
12.63.
Find and interpret mean
Find and interpret standard deviation
Answer:
i dont know 69 420?
Step-by-step explanation:
23 x 5 + 6 x 50 -7 = ?
Answer: Your anwser would be 408 please mark brainliest thank you
Step-by-step explanation:
Answer:408
Step-by-step explanation:
To find the answer, we can use the order of operations ( PEMDAS)
23*5=115
6*50=300
so simplified
115+300-7
add
415-7
subtract
408
so 23*5+6*50-7=408
Find the unknown angle in the figure
Answer:
Angle 145 degrees
Step-by-step explanation:
Hope it can help you lovelots
Hello Please help me.
Answer:
Step-by-step explanation:
1) D
2) B
3) no solution
y ≤ 0.5x - 4 is area C including the red line
y ≥ 0.5x + 5 is area A including the blue line
The scatter plot shows a regression line of advertising dollars spent and sales. If the company were to spend $6,500 on advertising, what would be the predicted sales?
A) $110,000
B) $114,000
C) $118,000
D) $122,000
HELPPP PLEASE IM GIVING OUT BRAINLIEST
Answer:
C
Step-by-step explanation:
so 13+139+123+129 so WHAT does this =
Answer:
404
Step-by-step explanation:
you just add numbers you know first
Please take a look at the picture
Answer: C
Step-by-step explanation:
How many ⅖ are in 1½
Answer:
3 (remainder 3)
Step-by-step explanation:
One snowy day, the snow was falling at a rate of 3 inches per hour.
If it kept snowing at the same rate, now many inches would
accumulate in 24 hours
artice
соо
Answer:
72 inches
Step-by-step explanation:
You would multiply the 3 inches per hour times the 24 hours to get 72 inches of snow.
Answer:
72 Inches
Step-by-step explanation:
24x3=72
what is one third the product of 2 numbers a and b.
Answer:
1/3 (a+b)
Step-by-step explanation:
The required solution is 1/3ab.
It is required to find the solution.
What is arithmetic?Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.
Given:
Let the 2 numbers be a and b.
According to given question we have,
Product =a× b=ab
1/3 of product =1/3ab
Therefore, the required solution is 1/3ab.
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Write a ratio for 2 batches of this recipe.
A line that passes through the points (12,12) and (20,6)
Answer:
8,48 I think
Step-by-step explanation:
I subtracted them from each other
The required equation of the line is given as y = -6x / 8 + 21.
Given that,
A line that passes through points (12,12) and (20,6)
The slope of the line is a tangent angle made by line with horizontal. i.e. m = tanx where x in degrees.
here,
Standard equation of the line,
y -y₁ =(y₂ - y₁) / (x₂ - x₁) (x - x₁)
Substitute the point in the above equation,
y - 12 = (6-12)/(20 - 12)[x - 12]
y = -6/8[x - 12] + 12
y = -6x/8 +9 + 12
y = -6x / 8 + 21
Thus, the required equation of the line is given as y = -6x / 8 + 21.
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Two sides of a triangle measure 27 inches and 32 inches.
Which could represent the length of the third side?
Answer options:
5 in
59 in
7 in
62 in
Answer:
62 in
Step-by-step explanation:
the Hypotenuse of a triangle is always longer than the two other sides, 27 + 32 is larger than all but one of the options, 62. Making 62 the answer by process of elimination.
Find the surface area of this cuboid
Answer:
62
Step-by-step explanation:
SA=2(5x2)+2(5x3)+2(3x2)
SA=20+30+12
SA=62
Which symbol correctly compares the numbers?
-0.64 0-0.5
O>
O <
O I don't know.
Answer:
<
Step-by-step explanation:
-0.5 is greater than -0.64
We need to find the symbol -0.64 ,0-0.5. -0.64<0-0.5.
What is Number system?A number system is defined as a system of writing to express numbers.
We need to find which symbol is used between Minus zero point six four and minus zero point five.
-0.64 and -0.5
As we know that the integers are number with positive, Negative and zero.
-0.64<-0.5
On the number line the integer -0.64 lies on left of -0.5.
So -0.64 is less than -0.5.
Hence -0.64 is less than -0.5.
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what is this simplified as a fraction
Step-by-step explanation:
35/48
this cannot be simplified any further
pls help me find the missing angle
Answer:
b=114
c=43................
Gven: f(x) = 4x +1 and (x)= x^2 + 1.
find (fog)(x)
Answer:
Step-by-step explanation:
27836?+_68_729+_8978
A 52-centimeter-long board is cut into 3 pieces. The longest piece is twice as long as the shortest piece. The other piece is 4 cm longer that the shortest piece. How long is each piece?
Answer:
4c 6th fastest 9.I gghiii
Help pls asap!!! Make sure to answer all of them!
Answer:-4
-3
-2
Step-by-step explanation:
thx
п
What is the end behavior of the polynomial function?
1
8
B
4
2
6
2
2
8
B
X
-4
6
o As X->-co, then Y---
As X-→-00, then y0
As X-0, then y →-00
ne X -> then V -> 0
Answer:
The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity
Step-by-step explanation:
hope this help
dont know if this is correct
The end behavior of the polynomial function is as x -> ∞, y -> -∞
How to determine the end behavior?From the graph of the polynomial, we have the following highlight:
As x approached infinityThe function approaches negative infinityThe above highlights mean that:
As x -> ∞, y -> -∞
Hence, the end behavior of the polynomial function is as x -> ∞, y -> -∞
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Please take a look at the picture
Answer:
I think it'
is A and B
Step-by-step explanation:
hope hwlps
Please take a look at the picture
Answer:
B) -g/-h
Step-by-step explanation:
-g/-h=g/h
Rewrite the fraction.
-(-g/h) = g/h
Hope this helps :)
For homework, Tina is asked to write down the opposite value for each number listed. Which comparison did Tina write incorrectly?
Answer:
x
Step-by-step explanation:
It still would be a negative.
The comparison that Tina wrote incorrectly is X. Then the correct option is B.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The table is given below.
Comparison Number Opposite value
W -3 3
X -(-9) 9
Y 0 0
Z 4 - 4
The number -(-9) is also written as 9 and the opposite number of 9 is negative 9. Then the comparison that Tina wrote incorrectly is X. Then the correct option is B.
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What's the kinetic energy of an object that has a mass of 12 kilograms and moves with a velocity of 10 m/s?
Answer:
Step-by-step explanation:
Assuming it has no spin
KE = ½mv²
KE = ½(12)10²
KE = 600 J
the length of a rectangle in (3+√7) and it's with is (1+2√7). what is the area of the rectangle? what is the perimeter of the rectangle
Answer:
Area: (3+√7) x (1+2√7) = 17+7√7 = 35.52
Perimeter: 2(3+√7) + 2(1+2√7) = 8+6√7 = 23.87
A rectangular poster has a area of 504 centimeters. The width of the poster is 14 centimeters. How long is the poster?
Answer:
36 cm
Step-by-step explanation:
504/14=36
A jet is flying in a direction N 70° E with a speed of 600 mi/h. Find the north and east components of the velocity. Round to two decimal places.
Using vector concepts, it is found that the components of the velocity are given as follows:
North: 205.21 mi/h.East: 563.82 mi/h.How can a vector be represented in i and j notation?Given a magnitude M and angle [tex]\theta[/tex], the a vector V can be represented as follows:
[tex]V = M\sin{\theta}i + M\cos{\theta}j[/tex]
In which:
i is the horizontal(east/west) component.j is the vertical(north/south) component.In this problem, we have that the magnitude and the angle are given as follows:
[tex]M = 600, \theta = 70^{\circ}[/tex]
Hence the north component is:
[tex]600\cos{70^{\circ}} = 205.21[/tex]
And the east component is:
[tex]600\sin{70^{\circ}} = 563.82[/tex]
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Mr Harrison is 9 months old. How old is Mr Harrison daughter in days
Answer:
273.75 days
Step-by-step explanation: