MATHEMATICS HIGH SCHOOL

The distribution of heights for adult men in a certain population is approximately normal with mean 70 inches and standard deviation 4 inches. Which of the following represents the middle 80 percent of the heights ? A. 2.5% B. 5% C. 16% D. 1%

Answers

Answer 1

Answer:

The interval that represent the middle 80% of the heights (inches) is [64.88, 75.12].

Step-by-step explanation:

Given :

Mean -- $\rm \mu = 70 \; inches$

Standard Deviation -- $\rm \sigma = 4 \; inches$

Calculation :

We want to know an interval in which the probability that a height falls there is 0.8.

In such interval, the probability that a value is higher than the right end of the interval is

$\rm P(x>z) = \frac {1-0.8}{2} = 0.1$

If x is the distribuition of heights, then we want y such that P(x > y) = 0.1.

$Z = (x-\mu)/(\sigma)$

Now, let

$U = (y-70)/(4)$

We have

$\rm 0.1 = P(x>y)= P((x-70)/(4) > (y-70)/(4))=P(Z>U)=1-\phi(U)$

$\phi (U) = 1-0.1=0.9$

by looking at the table, we find that U = 1.28, therefore

$(y-70)/(4)=1.28$

$1.28* 4 + 70 = y$

$y=75.12$

The other end of the interval is the symmetrical of 75.12 respect to 70, hence it is

70- (75.12-70) = 64.88.

The interval that represent the middle 80% of the heights (inches) is [64.88, 75.12].

For more information, refer the link given below

brainly.com/question/10729938?referrer=searchResults

Answer 2

Answer:

Answer:

The interval (meassured in Inches) that represent the middle 80% of the heights is [64.88, 75.12]

Step-by-step explanation:

I beleive those options corresponds to another question, i will ignore them. We want to know an interval in which the probability that a height falls there is 0.8.

In such interval, the probability that a value is higher than the right end of the interval is (1-0.8)/2 = 0.1

If X is the distribuition of heights, then we want z such that P(X > z) = 0.1. We will take W, the standarization of X, wth distribution N(0,1)

$W = (X-\mu)/(\sigma) = (X-70)/(4)$

The values of the cumulative distribution function of W, denoted by $\phi$ , can be found in the attached file. Lets call $y = (z-70)/(4)$ . We have

$0.1 = P(X > z) = P((X-70)/(4) > (z-70)/(4)) = P(W > y) = 1-\phi(y)$

Thus

$\phi(y) = 1-0.1 = 0.9$

by looking at the table, we find that y = 1.28, therefore

$(z-70)/(4) = 1.28\nz = 1.28*4+70 = 75.12$

The other end of the interval is the symmetrical of 75.12 respect to 70, hence it is 70- (75.12-70) = 64.88.

The interval (meassured in Inches) that represent the middle 80% of the heights is [64.88, 75.12] .

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Answers

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Answers

Answer:

y = 8

x = 3

Step-by-step explanation:

5x+y=23

3x+y=17

cancel out the Xs

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Plug in 8 for the Y in any of the equations it doesn't matter

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M(5, 7) is the midpoint of RS. The coordinates of S are (6, 9). What are the coordinates of R?

Answers

Answer:

The coordinates of R are $(x_1,y_1)=(4,5)$

Step-by-step explanation:

Given : M(5, 7) is the midpoint of RS. The coordinates of S are (6, 9).

To find : What are the coordinates of R?

Solution :

We have given,

A line RS which has a mid point M.

Let, the coordinates of R be $(x_1,y_1)$

The coordinates of S are $(x_2,y_2)=(6, 9)$

The coordinates of M are $(x_3,y_3)=(5,7)$

Applying mid-point formula,

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Solve separately,

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y- coordinate is

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$y_1=5$

So, The coordinates of R are $(x_1,y_1)=(4,5)$

Coordinate R is at (4,5)

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Answers

Answer:

Factor:

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Answers

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