1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
MAVERICK [17]
3 years ago
14

Assume that the heights of adult Caucasian women have a mean of 63.6 inches and a standard deviation of 2.5 inches. If 100 women

are randomly​ selected, find the probability that they have a mean height greater than 63.0 inches. Round to four decimal places.
Mathematics
1 answer:
andrew-mc [135]3 years ago
7 0

Answer:

0.9918 = 99.18% probability that they have a mean height greater than 63.0 inches.

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

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 pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation, which is also called standard error s = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\mu = 63.6, \sigma = 2.5, n = 100, s = \frac{2.5}{\sqrt{100}} = 0.25

Find the probability that they have a mean height greater than 63.0 inches.

This is 1 subtracted by the pvalue of Z when X = 63. So

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{63 - 63.6}{0.25}

Z = -2.4

Z = -2.4 has a pvalue of 0.0082

1 - 0.0082 = 0.9918

0.9918 = 99.18% probability that they have a mean height greater than 63.0 inches.

You might be interested in
1. Create a circle. Show and explain the difference between the following:
liberstina [14]
1. 
a.
A secant line is a line which intersects the circle at 2 different points. 

A tangent line is a line which has only one point in common with the circle.

Check picture 1: The orange line s is a secant line, the blue line t is a tangent line.


b.
An inscribed angle is an angle formed by using 3 points of a circle. 

The main property of an inscribed angle is that its measure is half of the measure of the arc it intercepts.

Check picture 2: If  m(\angle KML)=\beta, then the measure of arc KL is 2 \beta.

A central angle is an angle whose vertex is the center of the circle, and the 2 endpoints of the rays are points of the circle.

The main property is: the measure of the central angle is equal to the measure of the arc it intercepts. 

Check picture 2

2.
To construct the inscribed circle of a triangle, we first draw the 3 interior angle bisectors of the triangle.
They meet at a common point called the incenter, which is the center of the inscribed circle.
We open the compass, from the incenter, so that it touches one of the sides at only one point. We then draw the circle. (picture 3)

To draw the circumscribed circle, we first find the midpoints of each side. We then draw perpendicular segments through these (the midpoints.) They meet  at one common point, which is the circumcenter: the center of the circumscribed circle.
We open the compass from the circumcenter to one of the vertices of the triangle. We draw the circle, and see that it circumscribes the triangle.

(picture 4)

3.

Given an equation of a circle: x^2-2x+y^2+6y+6=0.

To determine the center and the radius of the equation we must write the above equation in the form :

                              (x-a)^2+(y-b)^2=r^2.

Then, (a, b) is the center, and r is the radius of this circle. We do this process by completing the square.

Note that x^2-2x becomes a perfect square by adding 1, and 
y^2+6y becomes a perfect square by adding 9. 

Thus we have:

x^2-2x+y^2+6y+6=0\\\\(x^2-2x+1)+(y^2+6y+9)-4=0\\\\(x-1)^2+(y+3)^2=2^2

Thus, the center is (1, -3), and the radius is 2.

4. Not complete


5.

The radius of the pizza is \displaystyle{ \frac{131}{2}ft=65.5ft.

The surface of a circle with radius r is given by the formula \displaystyle{  A=\pi r^2,
and the circumference is given by the formula C=2πr.

Thus, the area of the whole pizza is given by \displaystyle{  A=\pi r^2= \pi\cdot65.5^2=4290.25 \pi (square ft).

Each of the 50 slices, has an area of \displaystyle{ \frac{4290.25 \pi}{50} =85.805 \pi (square ft)

Notice that the perimeter (the crust) of a slice is made of 2 radii, and the arc-like part.
The arc is 1/50 of the circumference, so it is \displaystyle{\frac{2 \pi r}{50} = \frac{2\cdot65.5\cdot \pi }{50}= 2.62 \pi.

So the perimeter of one slice is 65.5+65.5+2.62π=131+2.62π

7 0
3 years ago
Urgent, please i will give brainliest
Ne4ueva [31]

Answer:

1. \frac{\sqrt{13} }{3}

2. 3.2362

3. \frac{60}{11}

Step-by-step explanation:

1.

Cot is the trigonometric ratio defined by "adjacent" over "opposite". <em>So, adjacent = 2 and opposite = 3.</em>

By pythagorean theorem, we have the "hypotenuse" as  \sqrt{2^2+3^2}=\sqrt{13}

Csc is defined as the trig ratio "hypotenuse" over "opposite". <em>We know the sides, so Csc \theta = \frac{\sqrt{13} }{3}</em>

<em />

<em>First answer choice is right.</em>

<em />

2.

By definition, Csc \theta is the inverse of Sine \theta. <em>If given the value of sin theta, to find value of csc theta, we take the reciprocal of it. Hence:</em>

Csc\theta=\frac{1}{0.3090}\\=3.2362

Third answer choice is right.

3.

By definition tan and cot are inverse of each other. <em>So the value of tan is the reciprocal of the value of cot.</em> We can simply "flip" the value of tan theta to get the value of cot theta. Hence:

Cot\theta=\frac{60}{11}

Third answer is right.

3 0
3 years ago
Read 2 more answers
Y = -3x-2 Slope intercept form
lana66690 [7]

Answer:The equation of any straight line, called a linear equation, can be written as: y = mx + b, where m is the slope of the line and b is the y-intercept. The y-intercept of this line is the value of y at the point where the line crosses the y axis.

Step-by-step explanation:

4 0
3 years ago
Which of the following is a defined term? <br> Plane<br> Point<br> Line<br> Angle
mr_godi [17]
A line is a defined term
5 0
3 years ago
What value of n make this equation true 12(n+6)=96
exis [7]

Answer:

2

Step-by-step explanation:

(6+2)x 12 =96

5 0
3 years ago
Read 2 more answers
Other questions:
  • There are 491 people attending an ice hockey games that people are seated in sections with 30 seats in each section how many sec
    12·1 answer
  • What is the area? I need the answer now​
    8·1 answer
  • State if the polygons are similar
    9·1 answer
  • 3) The coordinates of point A are (−3, 6) and the coordinates of point B are (3, −6). Find the slope of AB
    10·2 answers
  • Round 0.051866 to 2 signatures figures please
    13·2 answers
  • Someone please help me
    13·1 answer
  • Solve this problem I'm confused <br> 3y-9x=27
    11·2 answers
  • Which statement about triangles is NOT true?
    14·1 answer
  • Determine whether a quadratic model exists for the set of values below. If​ so, write the model. f(0) = -4, f(3) = -19, f(-1) =
    12·1 answer
  • The cost of admission to the spring carnival was $39 for a group of 8 children and 3 adults. The admission was $43 for another g
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!