Adult male heights are a normal random variable with mean 69 inches and a standard deviation of 3 inches. Find the height, to the nearest inch, for which only 8 percent of adult males are taller (i. find the 92nd percentile)
Answers
Answer:
The height (corresponding to the \( \\ 92^{nd}\) percentile) is (to the nearest inch) 73 inches (and, approximately, only 8% of adult males are taller than this height.)
Step-by-step explanation:
Roughly speaking, the \( \\ 92^{nd}\) percentile is the x value (in the distribution) for which 92% of the observations in the [normal] distribution are below this x value, and 8% of the observations are above this x value.
To answer this question, we already know that:
Heights are a normal random variable, i.e, it follows a normal distribution.The mean for this distribution is \( \\ \mu = 69\) inches.The standard deviation is \( \\ \sigma = 3\) inches.Strategy for solving the question
For solving this, we have to use here the following key concepts: z-scores, the cumulative standard normal distribution, and the cumulative standard normal table.
Z-scores
To find the \( \\ 92^{nd}\) percentile, we can use z-scores or standardized values. A z-score is a value that tells us the distance in standard deviations units from the mean. When the z-score is positive, it means that the value is above the mean. A negative indicates that the z-score is below the mean. The formula to obtain a z-score is as follows:
\( \\ z = \frac{x - \mu}{\sigma}\) [1]
Where
z is the z-score.x is the raw score.\( \\ \mu\) is the mean.\( \\ \sigma\) is the standard deviation.Cumulative standard normal distribution and corresponding table
We still need to know the corresponding z-score, z, for the cumulative probability of 92%. For this, we have to consult the standard normal table, available on the Internet or in any Statistics books.
In this case, we look in the different columns of the standard normal table a probability value (exact or approximate) to 0.92 and then find the value for z that corresponds to this probability. The value for z is between 1.40 (0.91924) and 1.41 (0.92073).
Using z = 1.40 in [1], we have:
\( \\ z = \frac{x - \mu}{\sigma}\)
\( \\ 1.40 = \frac{x - 69}{3}\)
Then, solving for x:
Multiplying by 3 at each side of the equation:
\( \\ 1.40 * 3 = x - 69\)
Adding 69 at both sides of the equation:
\( \\ (1.40 * 3) + 69 = x\)
\( \\ x = (1.40 * 3) + 69\)
\( \\ x = 4.20 + 69\)
\( \\ x = 73.20\)
That is, the \( \\ 92^{nd}\) percentile is 73.20 inches, and to the nearest inch, this percentile is 73 inches.
This result indicates that, approximately, 92% of the heights are below 73 inches, and only 8% of heights are taller than this height.
The shaded area in the graph below shows an area of 0.08076 (8.076%) for 73.20 inches.
Related Questions
Does the point (8, 1) satisfy the inequality y
yes
no
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Sarah saved 12.00 dollars buying clothes. The cloth was on sale for 30% off. What was the original price?
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Problem
Sarah saved 12.00 dollars buying clothes. The cloth was on sale for 30% off. What was the original price?
Solution
For this case we know that 12.00 represent the 30% of the total price so we can set up the following proportional rule:
12/30 = x/100
And solving for x we got:
x= 100 (12/30)= 40$
And then the best answer would be:
40.00$
Type the expression that results from the following series of steps:
Start with n and divide by 2.
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Need help!!!!! with this test pls IM SORRY FOR ASKING SO MANY TIMES BUT PLS HELP
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Answer:
I hope its 15/10
Step-by-step explanation:
please let me know if its wrong
The graph of line l is shown below.
Which of the following is an equation for a line that is perpendicular to line l in the graph?
Y = –3x
Y = 3x – 5
Y = 1/3x
Y = x + 3
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A woman bought S shirts at $20 each and J jerseys at $ 15 each at a total Cost of $ 155. if however she had bought half as many Shirts, and twice as many jerseys, then the total Cost would have been $190. Evaluate S and J.
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After solving the set of linear equation so formed, we conclude that value of "S" and "J" is 4 and 5 respectively.
As per the question statement, A woman bought "S" shirts at $20 each and "J" jerseys at $ 15 each at a total Cost of $ 155. However, the total cost would have been $190 if she had purchased half as many shirts and twice as many jerseys. We are supposed to find the value of "S" and "J"
Let us first form the set of linear equation so formed.
Cost of one shirt = $20
Cost of "S" shirts = $20 x S = 20S
Cost of one jersey = $15
Cost of "J" jerseys = $15 x J = 15J
Total cost = $155
20S + 15J = 155 is our first linear equation obtained.
Now if however she bought half as many Shirts, and twice as many jerseys, then the total Cost would have been $190 and the equation formed will be :
20(S/2) + 15(2*J) = 190
or 10S + 30J = 190, is our second equation
This question is a classic example of forming a set of linear equation in two variable out of any given statement.
Solving the two sets of equation we get, S = 4 and J = 5
Linear equation: An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation and if it is equation in two variables then both the variables will have linear power or power 1.To learn more about linear equation, click on the link given below:
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Select all statements that are true.
Answers
Answers:
A, B, D, E
Nearly everything except choice C is true.
====================================================
Explanation:
Choice A is true because sine = opposite/hypotenuse.Choice B is true as well because cosine = adjacent/hypotenuseTangent is opposite/adjacent. The 4/9 should be 9/4. Therefore, choice C is false. If beta was theta, then tan(theta) = 4/9 would be true.Choice D is true because of the pythagorean theorem a^2+b^2 = c^2.Choice E is true because tan = opposite/adjacent, and the 9 and 4 are in the correct order (see choice C).Find the average rate of change for the function f(x)=3x+17
Using the intervals of x=3 to x=6
Show ALL your work to receive credit
Answers
Answer: what unit is this?
Step-by-step explanation:yeah I’ll need the unit to solve this question
please help I'll give brilliantist:)
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find the percent change from 62 to 7
Answers
Answer: 11.29
Step-by-step explanation:
A spinner is divided into 10 congruent sections.Each section is labeled with a number as shown.What is the probability that the arrow will land in a section that is labeled with a number that is a multiple of 2?
Answers
Answer:
50%
Step-by-step explanation:
The only numbers that are multiples of 2 are all even numbers. From 1 to 10 there are a total of 5 even numbers, meaning that only 5 sections are multiples of 2. Therefore, the probability of the arrow landing in a section that is labeled with a number that is a multiple of 2 would be
5/10 if we simplify this it would be 1/2 or 50%
Finally, we can say that the probability of the arrow landing on one of these sections is 50%
Answer:
20% or 1/5 or 0.2
Step-by-step explanation:
i took the test
Solve for b.
Ab + c = d
B= (d-c)/a
B= a + c/d
B= a/c-d
Answers
B= (-c+d)/a
Answer:
B
Step-by-step explanation:
just took this test
Point a is located at (2,6) and D is located at (-4, 10)
Answers
Alyssa has 9 markers and 24 pencils what is the most numbers of kits she can make of each kit has the same number of items?
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In 1990, there were 4,298,000 Mexican immigrants living in the United States. In 2000 this number had increased to 7,858,000. Find the percent of increase to the nearest tenth. a. 69.6% c. 82.8% b. 101% d. 90.2%
Answers
Answer:
c
Step-by-step explanation:
In thousands:
\(7858 - 4298 = 3560\)
\( \frac{3560}{4298} = .828\)
\(4298 \times 1.828 = 7857\)
help plssss plssss !!1
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Answer:
were u looking for some like this, its for the first question
Step-by-step explanation:
Answer: F=.36
G=--1.36
H=1.36
J=1.36
Step-by-step explanation:
find the classical probability of spinning 3
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Answer:The probability of spinning a 3 is also 2 / 8.
I need help can somebody help me
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Answer:
2(9x-3)
6(3x-1)
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Which models show the problem 4/6 : 2/6 = 2? Check all that apply :
Answers
Answer: 1st, 2nd, and 3rd option are correct :) ✨
Step-by-step explanation:
Answer:
A, B, C
Step-by-step explanation:
4. Sketch the graph of F(x) = 1 +x/x²-1
Answers
The graph of the function is attached below.
What is the graph of a function?The graph of a function shows the correlation between its inputs (represented by x-values) and matching outputs (represented by y-values). It is a means of illustrating the actions and traits of a function.
Plotting points that conform to the function's rule in a cartesian coordinate system results in the graph of the function. An input-output pair for the function is represented by each point on the graph. The point's x-coordinate represents the input value, while its y-coordinate represents the output value.
We can further use the graph to determine the range, domain, y-intercept, x-intercept and so many others from a graph.
In the given problem;
The graph of the function f(x) = 1 + x / x² - 1 is attached below;
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(B^2)(B^4)
Answer choices
B^8
B^6
B^2
2b^6
Answers
Answer:
Step-by-step explanation:
(B^2)(B^4) = B^(2+4)= B^6
answer is B
What is p2 + 13 if p = −4?
29
17
−3
−21
Answers
The value of the expression p² + 13 will be A. 29.
How to compute the expression?It should be noted that the expression given is that p² + 13 and we are told that p = -4.
Therefore, we have to put the value of p into the expression. This will be:
p² + 13
= (-4)² + 13
= 16 + 13.
= 29
The value is 29.
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I need help with this homework packet
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a. The probability that a yellow disk will be selected is 1 out of 5.
b. It is **likely** that a yellow disk will be randomly selected from the bag.
What is the probability that a yellow disk will be selected?a. The probability that a yellow disk will be selected can be calculated by;
P = 5 / 25
P = 1/5
The probability of randomly selecting a yellow disk is calculated by dividing the number of yellow disks by the total number of disks. In this case, there are 5 yellow disks and 25 total disks, so the probability is 5/25 = 1/5. This means that there is a 20% chance of randomly selecting a yellow disk.
b. The likelihood of randomly selecting a yellow disk is described as "likely" because the probability is greater than 1/10. A probability of 1/10 or less is considered "unlikely", while a probability of greater than 1/10 is considered "likely".
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simplify x^0 y^-3/x^2y^-1
Answers
The answer is 1/x^2y^2
The given expression is \( \frac{ {x}^{0} y { - }^{3} }{ {x}^{2}y { - }^{1} } \)
We know that any number raised with zero power equals 1. Thus, \( {x}^{0} = 1\)
Hence, the expression becomes
\( \frac{y { - }^{3} }{ {x}^{2} y { - }^{1} } \)
Now, apply the quotient rule,\( \frac{ {x}^{ \alpha } }{ {x}^{b} } = {x}^{ \alpha - b} \)
Using this rule, we have
\( \frac{1}{ {x}^{2} y { - }^{1 - ( - 3)} } \)
\( = \frac{1}{ {x}^{2} y { - }^{1 + 3} } \)
\(= \frac{1}{ {x}^{2} {y}^{2} } \)Hence, the simplified expression is \( \frac{1}{ {x}^{2} {y}^{2} } \)
Solve for x: 3(x+1) = -6
A.-2
B.-3
C. 1
D.7/3
Answers
Answer: x = -3
Step-by-step explanation:
3(x + 1) = -6
Divide both sides by 3: 3(x + 1) / 3 = -6 / 3
x + 1 = -2
Subtract 1 from each side: x + 1 - 1 = -2 - 1
x = -3
". At an ice cream parlor, ice cream cones cost $1.10 and sundaes cost
$2.35. One day, the receipts for a total of 172 cones and sundaes were
$294.20. How many cones were sold?
Answers
The number of cones and sundaes sold at the ice cream parlor is 88 and 84 respectively.
EquationThere are three basic types of equation in mathematics. Namely:
Linear equationsQuadratic equationsSimultaneous equationsCost of cones = $1.10Cost of sundaes = $2.35Total sold = 172Total cost = $294.20Number of cones = cNumber of sundaes = sc + s = 172
1.10c + 2.35s = 294.20
from (1)
c = 172 - s
substitute
1.10c + 2.35s = 294.20
1.10(172 - s) + 2.35s = 294.20
189.2 - 1.10s + 2.35s = 294.20
- 1.10s + 2.35s = 294.20 - 189.2
1.25s = 105
s = 105 ÷ 1.25
s = 84
Recall,
c + s = 172
c + 84 = 172
c = 172 - 84
c = 88
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A ship X sailing with a velocity (21 kmh 052⁰) observes a light fron a lighthuse due North. The bearing of the liglhthouse from the ship 20 minutes later is found to be 312. calcuate correct to thre sigificant figures
i) the orignal distance when the lighthoues is due West of the ship from the time when it is due North of the ship.
ii) the time in minutes, when the lighthouse is due West of the ship from the time when it is due North of the ship.
iii) the distance in km of the ship from the lighthoue when the light.hose is due West of the ship
Answers
i) the original distance when the lighthouse is due West of the ship is 7 km
ii) The time in minutes when the lighthouse is due West of the ship is 21 minutes
iii) The distance in km of the ship from the lighthouse when the lighthouse is due West of the ship is 29.97 km
To solve this problem, we'll use the concepts of relative velocity and trigonometry. Let's break down the problem into three parts:
i) Finding the original distance when the lighthouse is due West of the ship:
The ship's velocity is given as 21 km/h at a bearing of 052°. Since the ship observed the lighthouse due North, we know that the angle between the ship's initial heading and the lighthouse is 90°.
To find the distance, we'll consider the ship's velocity in the North direction only. Using trigonometry, we can determine the distance as follows:
Distance = Velocity * Time = 21 km/h * (20 min / 60 min/h) = 7 km (to three significant figures).
ii) Finding the time in minutes when the lighthouse is due West of the ship:
To find the time, we need to consider the change in angle from 052° to 312°. The difference is 260° (312° - 052°), but we need to convert it to radians for calculations. 260° is equal to 260 * π / 180 radians. The ship's velocity in the West direction can be calculated as:
Velocity in West direction = Velocity * cos(angle) = 21 km/h * cos(260 * π / 180) ≈ -19.98 km/h (negative because it's in the opposite direction).
To find the time, we can use the formula:
Time = Distance / Velocity = 7 km / (19.98 km/h) = 0.35 h = 0.35 * 60 min = 21 minutes (to three significant figures).
iii) Finding the distance in km of the ship from the lighthouse when the lighthouse is due West of the ship:
We can use the formula for relative velocity to find the distance:
Relative Velocity = sqrt((Velocity in North direction)² + (Velocity in West direction)²)
Using the values we calculated earlier, we have:
Relative Velocity = sqrt((21 km/h)² + (-19.98 km/h)²) ≈ 29.97 km/h (to three significant figures).
Therefore, the ship is approximately 29.97 km away from the lighthouse when the lighthouse is due West of the ship.
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Identify the unit rate in the graph.
A. 40mph
B. 75mph
C. 50mph
D. 25mph
Answers
Answer:
The unit rate is C. 50mph
Step-by-step explanation:
Take two points from the line,
I took points (1, 50) and (2, 100).
Then plug them into this formula:
y2-y1/x2-x1
Solve:
(100- 50)/(2 - 1)
100 - 50 = 50
2 - 1 = 1
50/1 = 50
So, you get C. 50mph
Answer:
The answer would be C. 50mph
Step-by-step explanation:
Got right on USA test prep
Hope this helps
Find three times five-twelfths, expressed as a decimal.
Answers
Answer:
The answer will be 1.25
Step-by-step explanation:
In order to make 512 into a decimal, you take the top number or numerator, which is 5 , and take your bottom number or your denominator, which is 12 , and divide 5 by 12 which will give you0.416666667
Hey there! :)
Answer:
1.25
Step-by-step explanation:
Begin by multiplying the fractions:
\(\frac{3}{1}* \frac{5}{12}= \frac{3*5}{1*12} = \frac{15}{12}= \frac{5}{4}\)
Convert \(\frac{5}{4}\) into a decimal:
5/4 = 1.25.
Which of the diagrams shows an exponential graph?
Answers
Answer:
Diagram "C"
Step-by-step explanation:
The curve eventually shows that it is an exponentially graph