1) Suppose the heights of 18-year-old men are approximately normally distributed, with mean 71 inches and standard deviation 5 inches.
a)
What is the probability that an 18-year-old man selected at random is between 70 and 72 inches tall? (Round your answer to four decimal places.)
b)
If a random sample of twenty-six 18-year-old men is selected, what is the probability that the mean height x is between 70 and 72 inches? (Round your answer to four decimal places.)
c)
Compare your answers to parts (a) and (b). Is the probability in part (b) much higher? Why would you expect this?
!) The probability in part (b) is much higher because the mean is larger for the x distribution.
!!) The probability in part (b) is much lower because the standard deviation is smaller for the x distribution.
!!!) The probability in part (b) is much higher because the standard deviation is smaller for the x distribution.
!!!!) The probability in part (b) is much higher because the mean is smaller for the x distribution.
!!!!!) The probability in part (b) is much higher because the standard deviation is larger for the x distribution.
2) Let x be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12 hour fast. Assume that for people under 50 years old, x has a distribution that is approximately normal, with mean = 66 and estimated standard deviation = 45. A test result x < 40 is an indication of severe excess insulin, and medication is usually prescribed.
a)
What is the probability that, on a single test, x < 40? (Round your answer to four decimal places.)
b)
Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x? Hint: See Theorem 6.1.
!) The probability distribution of x is approximately normal with x = 66 and x = 45.
!!) The probability distribution of x is approximately normal with x = 66 and x = 22.50.
!!!) The probability distribution of x is approximately normal with x = 66 and x = 31.82.
!!!!) The probability distribution of x is not normal.

c) What is the probability that x < 40? (Round your answer to four decimal places.)
d) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)
e) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to four decimal places.)
f) Compare your answers to parts (a), (b), (c), and (d). Did the probabilities decrease as n increased?
Yes
NO
g) Explain what this might imply if you were a doctor or a nurse.
!) The more tests a patient completes, the weaker is the evidence for lack of insulin.
!!) The more tests a patient completes, the stronger is the evidence for lack of insulin.
!!!) The more tests a patient completes, the weaker is the evidence for excess insulin.
!!!!) The more tests a patient completes, the stronger is the evidence for excess insulin.

Answer:

middle graph

Step-by-step explanation:

Soluton

The  second (middle ) graph is the only one that works.

The amount of interest after 3 years will be $15.

The complete question is given below.

You loaned a friend $100 and will charge him 5% annual simple interest when he pay it back. What is the amount of interest after 3 years?

Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.

The interest is given as

I = (P × R × T) / 100

Where, P is the initial amount, R is simple interest rate, and T is the time.

We have

P = $100

R = 5%

T = 3 years

Then the interest will be

I = (100 × 5 × 3) / 100

I = $15

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Answer:

Approximately $594.38

Step-by-step explanation:

Use the formula: y = a(1 + r)^t
a is the initial amount
r is the percent of interest in decimal form
t is the time in years
y is the money after t years

Substitute the values given in the problem into the equation:
400(1+0.02)^20
Use a calculator or solve manually
Around 594.38

Answer:

-2/7

Step-by-step explanation:

We can use the slope formula

m = ( y2-y1)/(x2-x1)

    = ( 1-3)/( 3 - -4)

    = (1-3)/( 3+4)

    = -2/7

Answer:

(2+6)/2= 4 (x-coordinate of midpoint)

(7+3)/2= 5(y=coordinate of midpoint)

Answer:

Hope it will help you:)

Step-by-step explanation:

Solution:

here,

A(2,7)-([tex]x_{1,}y_{1[/tex])

B(6,3)-([tex]x_{2},y_{2[/tex])

Now using midpoint formula,

midpoint of ab=(x1 + x2)/2, (y1 + y2)/2

                        =(2+6)/2,(7+3)/2

                         =(8/2,10/2)

                          =(4,5)

The midpoint of AB is(4,5).

The number of the meals possible is 350.

The complete question is given below:-

A menu has 5 choices of appetizers, ten main courses, and seven desserts. How many meals are possible?

The arrangement of the different things or numbers in a number of ways is called the combination.

Given that:-

The number of the combination of the meals will be calculated as:-

N = 5 x 10 x 7

N = 350

Therefore the number of the meals possible is 350.

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find hourly rate:

96 / 16 = 6 pounds per hour

6 x 1.5 = 9 pounds per hour for overtime.

9 x 4 = 36 pounds

96 + 36 = 132 pounds total

Answer:

20°

Step-by-step explanation:

take the sum of 3y + 10 and y and equal it to 90° that creates an equation making it easier for you to continue

Answer:

let's assume the opposite angle of Y to be X

angle Y = angle X ( vertically opposite angles)

3y + 10 + X + 90° = 180° ( forming linear pair)

3y + X + 100 = 180°

X + 3y = 80° ----(1)

Y + 3y = 80°

4y = 80°

y = 20°

Answer:

0 = 0 thats my answer

Step-by-step explanation:

Step-by-step explanation:

sorry sorry ^$£%£$¥#^÷£=₩€%¥=£=;÷¥÷¥9=

Answer:

converges

Step-by-step explanation:

well the two polynomials in the series are 1 and n^8 (I'm assuming the +7 is not in the decimal but it seems to not matter). The degree of the polynomial 1 is 0 which can be represented by 1x^0. The second polynomial in the denominator has a degree of 8. So j = 0  and k = 8. Since 0 < (8-1)

0 < 7 the series converges

Answer:

lol

79*540=lol haha

Step-by-step explanation:

then lol lala lol hahahaha hahaha ten another big lol get it lollalol

Answer:

oh.

Step-by-step explanation:

Answer:

2y - 9x

Step-by-step explanation:

2y + 3 ( x - 4x )

First, solve the brackets.

2y + 3x - 12x

Combine like terms.

2y - 9x

Answer:

[tex]\sf 2y-9x[/tex]

Step-by-step explanation:

Hi There Student! Let me help you out on this question.

________________________________________________________

In this problem, we are given an expression [tex]\longmapsto\pmb{2y+3(x-4x)}[/tex], and asked to simplify it.

                                    ↪

First, we can perform the operation inside the parentheses, x-4x:

[tex]\longmapsto\sf 2y+3(-3x)}[/tex].

Now we can multiply 3 times -3x:

[tex]\longmapsto\sf 2y-9x[/tex]

And that is our final answer, because 2y and -9x are not like terms.

Hope that this helped! Have a good day ahead.

Best Wishes!

[tex]\star\bigstar\overline{\overline{\underline{\underline{\textsf {Reach far. Aim high. Dream big.}}}}}\bigstar\star[/tex]

 ◆◈-Greetings!-◈◆

-______________________________

Answer:

339.47

Step-by-step explanation:

100 - 24 = 76

258 = 76 percent

3.39473684211 = 1 percent

339.47 = 100 percent

Answer:

The decrease in price is $61.92

The sale price is $196.08

Step-by-step explanation:

24% × 258 = 61.92

258 decrease 24% =

258 × (1 - 24%) = 258 × (1 - 0.24) = 196.08

The factorisation of the given algebraic expression is [tex]6a^{2} (5a^{4}-4 )[/tex].

The given expression is [tex]30a^{6} -24a^{2}[/tex].

We need to factorise the given expression.

Each of these numbers and expressions is referred to as a factor of algebraic expressions if it is possible to express algebraic expressions as the product of numbers, algebraic variables, or algebraic expressions.

Now, [tex]30a^{6} -24a^{2}=6a^{2} (5a^{4}-4 )[/tex]

Therefore, the factorisation of the given algebraic expression is [tex]6a^{2} (5a^{4}-4 )[/tex].

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Answer:

the answer is c

Step-by-step explanation:

Answer:

A. b+2(b+2b)

b + 2b + 4b = 7b

B. 3b + b = 4b

C. 2(2b) = 4b

None of them are equal to 9b

Answer:

[tex]\fbox {None}[/tex]

Step-by-step explanation:

A

B

C

Answer:

Step-by-step explanation:

hello :

y=x²-10x+16  in the form y=(x-h)²+k

y= x²-2(5)(x)+16  

y = x²-2(5)(x)+5²-9

y= (x-5)²-9    when h=5 and k = -9

Answer: B -60

Step-by-step explanation: When you plug in -60 into the equation it all equals out into -12 = -12, which is true. All of the other solutions don't work.

Answer:

B. x = -60

Step-by-step explanation:

8 + x/3 = 1/6 (x-6) - 1

Multiply both sides by 6.

48 + 2x = x - 6 - 6

x = -12 - 48

x = -60

Answer:

Run 4 hours, Walk 8 hours.

Step-by-step explanation:

Let R be the running time

Let W be the walking time

Distance = Speed x Time

48 = 6R + 3W (equation 1)

12 = R + W (equation 2)

We will use elimination method to solve for these simulteanous equations.

Multiply Equation 2 by 3.

12x3 = 3(R+W)

36 = 3R + 3W (equation 3)

now subtract equation 3 from equation 1.

48-36 = 6R - 3R + 3W - 3W

12 = 3R

R = 12/3

= 4hours

now Substitute R into equation 2.

12 = 4 + W

W = 12 - 4

= 8

Therefore Michael plan to run for 4 hours and walk for 8 hours.

Answer:

-26

Step-by-step explanation:

Multiply -4 by 7

1-20-7

Subtract 20 from 1

-19-7

Subtract 7 from -19

-26

The mean absolute deviation of the number of books is 1.84

The dot plot of the number of books is in the attached figure.

From the figure, we have:

x      f

1       1

2      2

3      2

4      3

5      1

6     2

7     3

8     1

Start by calculating the mean using:

[tex]\bar x= \frac{\sum fx}{\sum f}[/tex]

So, we have:

[tex]\bar x= \frac{1 * 1 + 2 * 2 + 2 * 3 + 3 * 4 + 1 * 5 + 2 * 6 + 3 *7 + 1 * 8}{1 +2+2+3+1+2+3+1}[/tex]

Evaluate the sum and products

[tex]\bar x= \frac{69}{15}[/tex]

Divide

[tex]\bar x= 4.6[/tex]

The mean absolute deviation is then calculated as:

[tex]|\bar x| = \frac{\sum f|x - \bar x|}{\sum f}[/tex]

So, we have:

[tex]|\bar x|= \frac{1 * |1 -4.6|+ 2 * |2 -4.6| + 2 * |3 -4.6|+ 3 * |4 -4.6|+ 1 *| 5 -4.6|+ 2 * |6 -4.6|+ 3 *|7 -4.6|+ 1 * |8-4.6|}{1 +2+2+3+1+2+3+1}[/tex]

Evaluate the absolute difference

[tex]|\bar x|= \frac{1 * 3.6+ 2 * 2.6 + 2 * 1.6+ 3 * 0.6+ 1 *0.4+ 2 * 1.4+ 3 *2.4+ 1 * 3.4}{15}[/tex]

Evaluate the sum of products

[tex]|\bar x|= \frac{27.6}{15}[/tex]

Divide

[tex]|\bar x|= 1.84[/tex]

Hence, the mean absolute deviation of the number of books is 1.84

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Answer:

10

Step-by-step explanation:

I don't know what the word or phrase is, but with the parameters you've given, 100%

[tex]\text{First I would recommend replacing the question mark with x}\\\text{We have two ratios, }\\\text{and we need to solve that hard-looking equation}\\\text{in terms of x}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\text{We can multiply x times 36:: 36x}\\\text{We can multiply 4 times 27:: 108}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\text{Now it's easier to solve for x:: 36x=108; x=3}\\\text{ (we divided by 36 on both sides of the = sign)}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\text{The missing number is 3}[/tex]

Answer:

1/4

Step-by-step explanation:

4/8 = 1/2

1/2 x 1/2 = 1/4