A doctor conducts a survey with a random sample of his patients, measuring their cholesterol levels in millimolar per liter.
The data measurements for 14 patients are given below. Assuming the population standard deviation is o = 1.3 and that
the population is normally distributed, compute a 90% confidence interval for the mean cholesterol levels of his patients.
Round your answers to two decimal places and use ascending order.

Answers

Answer 1

Using the z-distribution, as we have the standard deviation for the population, it is found that the 90% confidence interval for the mean cholesterol levels of his patients is (5.59, 6.73).

What is a t-distribution confidence interval?

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the sample.

In this problem, we have a 90% confidence level, hence[tex]\alpha = 0.90[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.

Researching on the internet, the other parameters are given by:

[tex]\overline{x} = 6.16, \sigma = 1.3, n = 14[/tex]

Hence:

[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 6.16 - 1.645\frac{1.3}{\sqrt{14}} = 5.59[/tex]

[tex]\overline{x} + z\frac{\sigma}{\sqrt{n}} = 6.16 + 1.645\frac{1.3}{\sqrt{14}} = 6.73[/tex]

The 90% confidence interval for the mean cholesterol levels of his patients is (5.59, 6.73).

More can be learned about the z-distribution at https://brainly.com/question/25890103


Related Questions

The magnitude of vector λ a is 5. Find the possible values of λ, if a=(5,12). Brainliest for correct answer. Look at photo.

Answers

Step-by-step explanation:

this is the answer for you

8) Evaluate this expression.

7.4 - (-3.7)

A) -3.7

B) 8.4

C) 11.1

D) 13.21

Answers

Answer:

C) 11.1

Step-by-step explanation:

7.4 -(-3.7)

- and - make +

7.4 + 3.7 = 11.1

Need help with this geometric question ASAP, Thank you

Answers

It would be an isosceles triangle. Consider both sides are equal the angles would have to be equal, creating an isosceles triangle.

Help please in picture below

Answers

Answer:

vertex is a point where two sides meet

fx=x^2-2x+8
I need some help with this math problem if you can give me the process

Answers

Answer:

x³/3 - x² + C

Step-by-step explanation:

∫ x² - 2x + 8 dx

= x³/3 - x² + C

when finding the derivative, you need to take the power plus 1 then divide by the power x^(2+1)/(2+1) = x³/3

the same goes for 2x and the 2/2 is 1 so you would get x²

since you are finding the derivative for x and 8 is a constant it equals zero.

when integrating you always need to add C at the end and C stands for a constant. The only time you do not add C is when the integral goes from one constant to the next.

Example: [tex]\int\limits^1_0 {x^2 - 3x +9} \, dx[/tex] like this...

PLEASE RATE!! I hope this helps!!

If you have any questions comment below

URGENT I NEED IT NOW PLEASE HELP ME!!!!

Answers

The fourth one because they at minimum need that amount not the most. The answer is option 4 or the last option

Brian buys a lawn ornament priced at $78. Shipping and handing are an additional 5% of the price. How much shipping and handing will Brain pay?

Answers

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{5\% of 78}}{\left( \cfrac{5}{100} \right)78}\implies 3.9[/tex]

Rosa invests $1100 in one account and $1300 in an account paying 3 % higher interest. At the end of one year she had earned $255 in interest. At what rates did she invest?

$1100 invested at __%

$1300 invested at __%

Answers

Answer:

$1100 at 9%$1300 at 12%

Step-by-step explanation:

The amount of interest earned in one year is the product of the interest rate and the amount invested at that rate. The total interest earned is the sum of the amounts of interest earned on each investment.

Let x represent the lower interest rate. Then the higher rate is x+0.03 and the total interest earned is ...

  1100x +1300(x+0.03) = 255

  2400x +39 = 255 . . . simplify

  2400x = 216 . . . . . . subtract 39

  x = 216/2400 = 0.09 = 9% . . . . divide by the coefficient of x

Rosa invested $1100 at 9%, and $1300 at 12%.

Please Help I have tried and can not get the correct answer

Find the x- and y-intercepts of the graph of the function f(x) = -4|x+1| +8
Enter your answers as points, (a,b)

Enter the x-intercepts in order of increasing x-value. if there are no x-intercepts, enter NA in both answer areas


x-intercepts: __________
__________
y-intercepts ___________

Answers

Answer:

(-3, 0) and (1, 0)

(0, 4)

Step-by-step explanation:

x-intercept is the point where y = 0.

y-intercept is the point where x = 0.

or points ...

f(x) = y = -4×|x + 1| + 8

let's start with the y-intercept (x = 0)

y = -4×1 + 8 = -4 + 8 = 4

the y-intercept point (only 1 point) is (0, 4).

for x = 0 the absolute value function contains 0+1. and that is always +1.

the x-intercept(s) :

0 = -4×|x + 1| + 8 (dividing by -4)

0 = |x + 1| - 2

|x + 1| = 2

because of the absolute value we have 2 possibilities :

+(x + 1) = 2

x + 1 = 2

x = 1

and

-(x + 1) = 2

-x - 1 = 2

-x = 3

x = -3

so the points of x-intercept are (-3, 0) and (1, 0)

the formula P=F/A,where P=pressure,F=force,andA=area,is used to caculate pressure.solve this formula for F

Answers

[tex]P= \dfrac FA \implies F = PA[/tex]

Find the area for all of them. Pleaseee help me I don’t understand.

Answers

Answer:

Step-by-step explanation:

top = 120sq m

middle = 17sq cm

bottom = 102 sq feet

Solve the following inequalities if it is known that function f is increasing on its domain f(4x-3)≥f(2-x^2), Df=(-8,4)

Solve the following inequalities if it is known that function f is decreasing on its domain f(5-x^2)≥f(3x-5), Df=(-∞,4)

Answers

The functions f(4x-3)≥f(2-x^2) and f(5-x^2)≥f(3x-5) are quadratic functions

The values of the inequalities are -5 ≤ x ≤ 1 and -5 ≤ x ≤ 2

How to solve the inequalities?

Inequality 1: f(4x - 3) ≥ f(2 - x^2), Df = (-8 , 4)

The function increases at (-8,4).

So, we have:

4x - 3 ≥ 2 - x^2

Rewrite as:

x^2 + 4x - 2 - 3 ≥ 0

Evaluate the like terms

x^2 + 4x - 5 ≥ 0

Expand

x^2 + 5x - x - 5 ≥ 0

Factorize the expression

x(x + 5) - 1(x + 5) ≥ 0

Factor out x + 5

(x - 1)(x + 5) ≥ 0

Solve for x

x ≥ 1 or x ≥ -5

Rewrite as:

-5 ≤ x ≤ 1

Inequality 2: f(5 - x^2) ≥ f(3x - 5), Df=(-∞,4)

The function decreases at (-∞,4).

So, we have:

5 - x^2 ≥ 3x - 5

Rewrite as:

x^2 + 3x - 5 - 5 ≤ 0

Evaluate the like terms

x^2 + 3x - 10 ≤ 0

Expand

x^2 + 5x - 2x - 10 ≤ 0

Factorize the expression

x(x + 5) - 2(x + 5) ≤ 0

Factor out x + 5

(x - 2)(x + 5) ≤ 0

Solve for x

x ≤ 2 or x ≤ -5

Rewrite as:

-5 ≤ x ≤ 2

Hence, the values of the inequalities are -5 ≤ x ≤ 1 and -5 ≤ x ≤ 2

Read more about inequalities at:

https://brainly.com/question/11234618

Can someone help me with this please

Answers

Answer:

6.46 seconds

Step-by-step explanation:

[tex] - 16 {t}^{2} + 65t + 248 = 0[/tex]

[tex]t = 6.46[/tex]

Write this ratio as a fraction in simplest form without any units six weeks to 18 days

Answers

Answer:

  7/3

Step-by-step explanation:

To write the ratio with no units. we need to have both parts of the ratio in the same units. That way the units cancel.

__

  6 weeks : 18 days = (6×7) days : (6×3) days = 7 : 3

The ratio as a fraction is ...

  (6 weeks)/(18 days) = 7/3

[tex] \rm \int_{0}^{ \pi } \cos( \cot(x) - \tan(x)) \: dx \\ [/tex]​

Answers

Replace x with π/2 - x to get the equivalent integral

[tex]\displaystyle \int_{-\frac\pi2}^{\frac\pi2} \cos(\cot(x) - \tan(x)) \, dx[/tex]

but the integrand is even, so this is really just

[tex]\displaystyle 2 \int_0^{\frac\pi2} \cos(\cot(x) - \tan(x)) \, dx[/tex]

Substitute x = 1/2 arccot(u/2), which transforms the integral to

[tex]\displaystyle 2 \int_{-\infty}^\infty \frac{\cos(u)}{u^2+4} \, du[/tex]

There are lots of ways to compute this. What I did was to consider the complex contour integral

[tex]\displaystyle \int_\gamma \frac{e^{iz}}{z^2+4} \, dz[/tex]

where γ is a semicircle in the complex plane with its diameter joining (-R, 0) and (R, 0) on the real axis. A bound for the integral over the arc of the circle is estimated to be

[tex]\displaystyle \left|\int_{z=Re^{i0}}^{z=Re^{i\pi}} f(z) \, dz\right| \le \frac{\pi R}{|R^2-4|}[/tex]

which vanishes as R goes to ∞. Then by the residue theorem, we have in the limit

[tex]\displaystyle \int_{-\infty}^\infty \frac{\cos(x)}{x^2+4} \, dx = 2\pi i {} \mathrm{Res}\left(\frac{e^{iz}}{z^2+4},z=2i\right) = \frac\pi{2e^2}[/tex]

and it follows that

[tex]\displaystyle \int_0^\pi \cos(\cot(x)-\tan(x)) \, dx = \boxed{\frac\pi{e^2}}[/tex]

It has been found that 50.3% of U.S. households own stocks and mutual funds. A random sample of 300 heads of households indicated that 171 owned some type of stock. At what level of significance in a two- tailed test would you conclude that this was a significant difference

Answers

Finding the p-value of the test using the z-distribution, as we are working with a proportion, it is found that this was a significant difference for levels of significance of 0.02 and lower.

What are the hypothesis test?

At the null hypothesis, we test if the proportion is of 50.3%, hence:

[tex]H_0: p = 0.503[/tex]

We have a two-tailed test, hence at the alternative hypothesis we test if the proportion is different, that is:

[tex]H_1: p \neq 0.503[/tex]

What is the test statistic?

The test statistic is given by:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.

In this problem, the parameters are:

[tex]n = 300, \overline{p} = \frac{171}{300} = 0.57, p = 0.503[/tex]

Hence:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.57 - 0.503}{\sqrt{\frac{0.503(0.497)}{300}}}[/tex]

[tex]z = 2.32[/tex]

What is the p-value?

Considering a two-tailed test, using a z-distribution calculator, the p-value is of 0.0203. Hence this was a significant difference for levels of significance of 0.02 and lower.

More can be learned about the z-distribution at https://brainly.com/question/26454209

how many 5 seater taxis do you need for78 people

Answers

Step-by-step explanation:

Answer: 78 /5 = 15.6 = 16 taxis. Step-by-step explanation: I HOPE THIS WILL HELP YOU AND MARK IT AS BRAINLIEST ANSWER PLEASE.

Donte is making brownies. For one batch, the recipe requires 1 5/6 cups of chocolate chips, and 1/6 cup of sugar. What is the combined amount, in cups, of chocolate chips and sugar that is used in one batch of brownies?​

Answers

Answer:

2

Step-by-step explanation:

1 ⅚ + ⅙ = 1 6/6, also known as, 2

The answer would be 2 cups, because
1 5/6 +1/6 = 1 6/6 or 2

Adding and subtracting I need it right now the answer

Answers

Answer:

Just give me the questions and ill do it

Step-by-step explanation:

a right triangle with a long leg (x+7) and a short leg with (x) and the hypothenuse is 13

Answers

Answer:

Area is 30cm^2 if thats what your asking

Step-by-step explanation:

Answer:

X = 5

Step-by-step explanation:

You need to use the Pythagorean theory to solve this question.

[tex] {13}^{2} = {x}^{2} + {(x + 7)}^{2} [/tex]

[tex]169 = {x}^{2} + ( {x}^{2} + 14x + 49)[/tex]

[tex]169 = 2 {x}^{2} + 14x + 49[/tex]

[tex]0 = 2 {x}^{2} + 14x + 49 - 169[/tex]

[tex]0 = 2 {x}^{2} + 14x - 120[/tex]

Now simply the equation by dividing everything by 2.

[tex]0 = {x}^{2} + 7x - 60[/tex]

[tex]0 = (x - 5)(x + 12)[/tex]

Now, you can find the possible solutions by setting each bracket to 0.

[tex]0 = x - 5[/tex]

[tex]5 = x[/tex]

OR

[tex]0 = x + 12[/tex]

[tex] - 12 = x[/tex]

However, a measurement on a triangle cannot be negative. Therefore, we can ignore -12 and say that the answer is x = 5.

Without dividing,
how can you tell if the quotient for
5,873 = 8 is greater than 700? Explain
whether the quotient is less than 800.

Answers

Answer:

The quotient is between 700 and 800

Step-by-step explanation:

Prove by multiplication

700*8 = 5600 < 5873

Similarly

800*8 = 6400 > 5873

So the expression is 5873/8

Now

We can prove the given statement to multiplication

Multiply with 8

700×85600

And

800×86400

Yes

We see 5873 lies between 5600 and 6400 hence the quotient is greater than 700 but less than 800

A cuple travels 420 miles to dr0p their dughter off at summer camp. The trip back has a short cut and is only 360 miles. And the gas mileage is 50% better
due to a lighter load. Write an expression for the total gas used and simplify.

Answers

The expression for the simplified total gas used is 1.43x.

How to write the expression of the total gas

let the gas used on the way to camp "x"

Then the gas used on the way back can be calculated as follows:

360 / 420 × 0.5 × x

To calculate the total fuel used, We need to add this to the 'x' used on the way.

Therefore,

total gas used = x + 360 / 420 × 0.5 × x = x + 0.43x = 1.43x

learn more on expression here: https://brainly.com/question/1462980

Which function grows at the fastest rate for increasing values of x?

g(x) = 10x + 15

f(x) = 2•3^x

h(x) = 5x^2 + x + 10

Answers

Answer:

The answer is g(x) = 10x + 15

Step-by-step explanation:

Given;g(x) = 10x + 15 f(x) = 2•3ˣ 5x² + x + 10To Find;function grows at the fastest rate for increasing values of x.

Here, If we assume the value of x is 1 we get,

g(x) = 10x + 15

g(1) = 10(1) + 15

g(1) = 10 + 15

g(1) = 35

Here, We get the answer 35.

Now,

f(x) = 2•3ˣ

f(1) = 2•3¹

f(1) = 2•3

f(1) = 6

Here, We get the answer 6.

Now,

h(1) = 5x² + x + 10

h(1) = 5(1)² + 1 + 10

h(1) = + 5 + 1 + 10

h(1) = + 16

Thus, The answer is g(x) = 10x + 15.

-TheUnknownScientist 72

How do I solve for y?

Answers

Answer:

Step-by-step explanation:

The angle containing y and 63 are vertically opposite. They are equal.

y + 23 = 63                   Subtract 23 from both sides

y +23-23 = 63 - 23

Answer y = 40

when a square's side is two units long,its perimiter is eight units

Answers

Answer:

Yes

Step-by-step explanation:

Because it has 4 sides and 4 x 2 = 8

HELP 50pts!!!
Ivanna drove 225 miles using 10 gallons of gas. At this rate , how many gallons of gas would she need to drive 441 miles ?

____ gallons

Answers

19.6 gallons

Explanation:

225 miles → 10 gallons1 miles → (10/225) gallons441 miles →  [ (10/225)*441 ] gallons441 miles → 19.6 gallons

Leslie’s puppy has 4 toys. Her cat has 36 toys.How many times more toys does the cat have than the puppy?
A.6
B.7
C8
D.9

Answers

D im pretty sure because 4x9=36

The statement "7 is 21 less than 28" is interpreted 7 = 21 - 28.​

Answers

it's interpreted as 28 - 21 = 7

Solve the system using elimination.

2x – 2y = –8
x + 2y = –1

(–3, 1)

(–14, 1)

(0, 4)

(1, 5)

Answers

Answer:

(- 3, 1 )

Step-by-step explanation:

2x - 2y = - 8 → (1)

x + 2y = - 1 → (2)

adding the 2 equations term by term will eliminate y

3x + 0 = - 9

3x = - 9 ( divide both sides by 3 )

x = - 3

substitute x = - 3 into either of the 2 equations and solve for y

substituting into (2)

- 3 + 2y = - 1 ( add 3 to both sides )

2y = 2 ( divide both sides by 2 )

y = 1

solution is (- 3, 1 )

Answer:

(–3, 1)

Step-by-step explanation:

Step 1: Solve for x

2x – 2y = –8 -----------(1)

x + 2y = –1. -------------(2)

Add equation 1 to 2

⇒2x + x| -2y + 2y |= -8 -1

⇒3x = -9

Divide both side by the coefficient of x

⇒3x/3 = -9/3

⇒x = -3

Step 2; Solve for y

Substitute into equation 2

x + 2y = –1

(-3) + 2y = -1

Add 3 from both sides

-3 + 2y + 3 = -1 + 3

2y = 2

divide both side by two

2y/2 = 2/2

y = 1

So, ( x,y) ⇒(-3,1)

Solve the equation X=

Answers

Step-by-step explanation:

I think the answer is x=70

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