Problem: The height, X, of all 3-year-old females is approximately normally distributed with mean 38.72
inches and standard deviation 3.17 inches. Compute the probability that a simple random sample of size n=
10 results in a sample mean greater than 40 inches. That is, compute P(mean >40).
Gestation period The length of human pregnancies is approximately normally distributed with mean u = 266
days and standard deviation o = 16 days.
Tagged
Math
1. What is the probability a randomly selected pregnancy lasts less than 260 days?
2. What is the probability that a random sample of 20 pregnancies has a mean gestation period of 260 days
or less?
3. What is the probability that a random sample of 50 pregnancies has a mean gestation period of 260 days
or less?
4. What is the probability a random sample of size 15 will have a mean gestation period within 10 days of
the mean?
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Answers

Answer 1

Answer:

0.1003 = 10.03% probability that a simple random sample of size n= 10 results in a sample mean greater than 40 inches.

Gestation periods:

1) 0.3539 = 35.39% probability a randomly selected pregnancy lasts less than 260 days.

2) 0.0465 = 4.65% probability that a random sample of 20 pregnancies has a mean gestation period of 260 days or less.

3) 0.004 = 0.4% probability that a random sample of 50 pregnancies has a mean gestation period of 260 days or less.

4) 0.9844 = 98.44% probability a random sample of size 15 will have a mean gestation period within 10 days of the mean.

Step-by-step explanation:

To solve these questions, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The height, X, of all 3-year-old females is approximately normally distributed with mean 38.72 inches and standard deviation 3.17 inches.

This means that [tex]\mu = 38.72, \sigma = 3.17[/tex]

Sample of 10:

This means that [tex]n = 10, s = \frac{3.17}{\sqrt{10}}[/tex]

Compute the probability that a simple random sample of size n= 10 results in a sample mean greater than 40 inches.

This is 1 subtracted by the p-value of Z when X = 40. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{40 - 38.72}{\frac{3.17}{\sqrt{10}}}[/tex]

[tex]Z = 1.28[/tex]

[tex]Z = 1.28[/tex] has a p-value of 0.8997

1 - 0.8997 = 0.1003

0.1003 = 10.03% probability that a simple random sample of size n= 10 results in a sample mean greater than 40 inches.

Gestation periods:

[tex]\mu = 266, \sigma = 16[/tex]

1. What is the probability a randomly selected pregnancy lasts less than 260 days?

This is the p-value of Z when X = 260. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{260 -  266}{16}[/tex]

[tex]Z = -0.375[/tex]

[tex]Z = -0.375[/tex] has a p-value of 0.3539.

0.3539 = 35.39% probability a randomly selected pregnancy lasts less than 260 days.

2. What is the probability that a random sample of 20 pregnancies has a mean gestation period of 260 days or less?

Now [tex]n = 20[/tex], so:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{260 - 266}{\frac{16}{\sqrt{20}}}[/tex]

[tex]Z = -1.68[/tex]

[tex]Z = -1.68[/tex] has a p-value of 0.0465.

0.0465 = 4.65% probability that a random sample of 20 pregnancies has a mean gestation period of 260 days or less.

3. What is the probability that a random sample of 50 pregnancies has a mean gestation period of 260 days or less?

Now [tex]n = 50[/tex], so:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{260 - 266}{\frac{16}{\sqrt{50}}}[/tex]

[tex]Z = -2.65[/tex]

[tex]Z = -2.65[/tex] has a p-value of 0.0040.

0.004 = 0.4% probability that a random sample of 50 pregnancies has a mean gestation period of 260 days or less.

4. What is the probability a random sample of size 15 will have a mean gestation period within 10 days of the mean?

Sample of size 15 means that [tex]n = 15[/tex]. This probability is the p-value of Z when X = 276 subtracted by the p-value of Z when X = 256.

X = 276

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{276 - 266}{\frac{16}{\sqrt{15}}}[/tex]

[tex]Z = 2.42[/tex]

[tex]Z = 2.42[/tex] has a p-value of 0.9922.

X = 256

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{256 - 266}{\frac{16}{\sqrt{15}}}[/tex]

[tex]Z = -2.42[/tex]

[tex]Z = -2.42[/tex] has a p-value of 0.0078.

0.9922 - 0.0078 = 0.9844

0.9844 = 98.44% probability a random sample of size 15 will have a mean gestation period within 10 days of the mean.


Related Questions

Mary Katherine has a bag of 3 red apples , 5 yellow apples and 4 green apples , Mary takes a red apples out of the bag and does not replace it. What is the probability that the next apple she takes out is yellow

Answers

Answer:

5/11.... you put the 5 which is yellow over the others which is 12 but remember she removed 1 so it would be equal to 11

Answer:

ok so if she takes a red apple out that means

2 red

5 yellow

4 green

11 in total

so 5/11

The answer is D

Hope This Helps!!!

Find the length of arc AB

Answers

Step 1: Find the circumference of the circle

Formula for circumference: C = 2 * pi * r

C = 2 * pi * 27

C = 54pi

Step 2: Find the length of the desired arc

We are only looking for 20 degrees out of 360 degrees, therefore we can multiply our circumference by 20/360.

20/360 * 54pi = 3pi units

Hope this helps!

What is the gradient of the blue line?

5
4
3
2
1
-5 -4 -3 -2 - 1 0 1. 2. 3. 4. 5
- 1
- 2
- 3
- 4
- 5




The line starts at (-5,3) and finishes (5,0.5)​

Answers

Answer:

The gradient is -0.25

Step-by-step explanation:

Given

[tex](x_1,y_1) = (-5,3)[/tex]

[tex](x_2,y_2) = (5,0.5)[/tex]

Required

The gradient (m)

This is calculated as:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

So, we have:

[tex]m = \frac{0.5-3}{5--5}[/tex]

[tex]m = \frac{-2.5}{10}[/tex]

[tex]m = -0.25[/tex]

Which statement is true about the equations
-3x + 4y = 12 and 1/4x-1/3y = 1

O The system of the equations has exactly one solution at (-8, 3).
O The system of the equations has exactly one solution at (-4, 3).
O The system of the equations has no solution; the two lines are parallel.
O The system of the equations has an infinite number of solutions represented by either equation.

Answers

The third option; solve the equation and get x=4+4/3y then substitute it into the first equation for x; -3( 4+4/3y) +4y=12 and solve to get no solution

Also, when you graph the two lines they are parallel

2) There are 40 boys and 60 girls in a class of students. What is the ratio of girls to students

Answers

Answer:

60:100, 6/10, 3/5, 6 to 10, etc.

Step-by-step explanation:

You take the number of girls over total students which is boys + girls. Since there's 40 boys and 60 girls, it's 60 girls to 100 students which can be written in several ways.

Answer:

60:100 / 3:5

Step-by-step explanation:

You first add the total number of students which is (40boys + 60girls) which gives us 100 students.

Then arrange the ratio of girls to students as per the question that is 60:100, reduce it to its lowest term that is dividing the ratio by 20, and finally got 3:5

Need help ASAP

HELP PLEASEE

Answers

a. Categorical
b. I think walking group (I’m not sure)
c. Bar graph

If 5x = 3x+12 then x = …..​

Answers

↦ [tex]\huge\underline{ \underline{Answer:-}}[/tex]

[tex]5x = 3x + 12 \\ 5x - 3x = 12 \\ 2x = 12 \\ x = \frac{12}{2} \\ x = 6[/tex]

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐

Step-by-step explanation:

Explanation is in the attachment

hope it is h helpful to you

Identify the effect on the graph of replacing f(x) by A f(x)

Answers

Answer:

See explanation

Step-by-step explanation:

Required

Effect of replacing [tex]f(x)[/tex] with [tex]f(x - h)[/tex]

f(x) is represented as: (x,y)

While

f(x - h) is represented as (x - h, y)

Notice the difference in both is that, the x value in f(x - h) is reduced by a constant h while the y value remain unchanged.

This means that the graph of f(x) will shift horizontally (i.e. along the x-axis) to the left by h units

f(x) = -16x^2 + 22x + 3

Answers

Answer:

factor???

Factored Form:  y= (-1)(8x+1)(2x-3)    

Step-by-step explanation:

Gemma recently rode her bicycle to visit her friend who lives 6 miles away. On her way there, her average speed was 16 miles per hour faster than on her way home. If Gemma spent a total of 1 hour bicycle, find the two rates.

Answers

first speed --- x mph

return speed -- x+16 mph

6/x + 6/(x+16) = 1

times each term by x(x+16)

6(x+16) + 6x = x(x+16)

x^2 + 4x - 96 = 0

(x-8)(x+12) = 0

x = 8 or x is a negative

her first speed was 8 mph

her return speed was 24 mph

check:

6/8 + 6/24 = 1 , that's good!

\int (x+1)\sqrt(2x-1)dx

Answers

Answer:

[tex]\int (x+ 1) \sqrt{2x-1} dx = \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{15}(2x-1)^{\frac{5}{2}} + C[/tex]

Step-by-step explanation:

[tex]\int (x+1)\sqrt {(2x-1)} dx\\Integrate \ using \ integration \ by\ parts \\\\u = x + 1, v'= \sqrt{2x - 1}\\\\v'= \sqrt{2x - 1}\\\\integrate \ both \ sides \\\\\int v'= \int \sqrt{2x- 1}dx\\\\v = \int ( 2x - 1)^{\frac{1}{2} } \ dx\\\\v = \frac{(2x - 1)^{\frac{1}{2} + 1}}{\frac{1}{2} + 1}} \times \frac{1}{2}\\\\v= \frac{(2x - 1)^{\frac{3}{2}}}{\frac{3}{2}} \times \frac{1}{2}\\\\v = \frac{2 \times (2x - 1)^{\frac{3}{2}}}{3} \times \frac{1}{2}\\\\v = \frac{(2x - 1)^{\frac{3}{2}}}{3}[/tex]

[tex]\int (x+1)\sqrt(2x-1)dx\\\\ = uv - \int v du[/tex]                              

[tex]= (x +1 ) \cdot \frac{(2x - 1)^{\frac{3}{2}}}{3} - \int \frac{(2x - 1)^{\frac{3}{2}}}{3} dx \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ u = x + 1 => du = dx \ ][/tex]    

[tex]= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{3} \int (2x - 1)^{\frac{3}{2}}} dx\\\\= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{3} \times ( \frac{(2x-1)^{\frac{3}{2} + 1}}{\frac{3}{2} + 1}) \times \frac{1}{2}\\\\= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{3} \times ( \frac{(2x-1)^{\frac{5}{2}}}{\frac{5}{2} }) \times \frac{1}{2}\\\\= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{15} \times (2x-1)^{\frac{5}{2}} + C\\\\[/tex]

2/9 divided by 5/6
help pleaseee​

Answers

Hey there!

[tex]\mathsf{\dfrac{2}{9}\div\dfrac{5}{6}}[/tex]

[tex]\mathsf{= \dfrac{2\times6}{9\times5}}[/tex]

[tex]\mathsf{2\times 6 = \bf 12}[/tex]

[tex]\mathsf{9\times5 = \bf 45}[/tex]

[tex]\boxed{\mathsf{=\bf \dfrac{12}{45}}}[/tex]

[tex]\large\textsf{BOTH NUMBERS has the Greatest Common Factor (GCF) of 3}[/tex]

[tex]\mathsf{= \dfrac{12\div3}{45\div3}}[/tex]

[tex]\mathsf{12\div3=\bf 4}[/tex]

[tex]\mathsf{45\div3=\bf 15}[/tex]

[tex]\boxed{\mathsf{=\bf \dfrac{4}{15}}}[/tex]

[tex]\boxed{\boxed{\large\textsf{Answer: }\mathsf{\bf \dfrac{4}{15}}}}\huge\checkmark[/tex]

[tex]\large\textsf{Good luck on your assignment and enjoy your day!}\\\\\\~\frak{Amphitrite1040:)}}[/tex]

Find the mean of the following data set.

8, 5, 15, 12, 10

A. 12.5
B. 10
C. 14
D. 50

Answers

Answer:

10

Step-by-step explanation:

the sum of 8,5,15,12,10 is 50 and there are 5 numbers so 50 divided by 5 is 10 and it's mean is also 10

hope this helps !

The answer is B/10 trust

Help meeee plzzzzzz!!!!

Answers

OPTION B is the correct answer.

Please help:

Given: ∠4 is congruent to ∠2
Prove: ∠3 and ∠1 are supplementary

Statements and Reasons

Answers

Answer:

See Below.

Step-by-step explanation:

We can write a two-column proof.

Statements:                                                Reasons:

[tex]\displaystyle 1)\, \angle 4\cong \angle 2[/tex]                                                   Given

[tex]\displaystyle 2)\, \angle 3 \cong \angle 4[/tex]                                                   Vertical Angles are Congruent

[tex]\displaystyle 3) \, \angle 1 + \angle 2 = 180[/tex]                                          Linear Pair

[tex]\displaystyle 4)\, \angle 1 + \angle 4 = 180[/tex]                                          Substitution

[tex]\displaystyle 5) \, \angle 1 + \angle 3 = 180[/tex]                                          Substitution

[tex]\displaystyle 6) \, \text{$\angle 3$ and $\angle 1$ are supplementary}[/tex]                  Definition of Supplementary Angles

A table is on sale for $247, which is 76% of the regular price.
What is the regular price?

Answers

Answer:

$325

Step-by-step explanation:

Find the regular price by dividing 247 by 0.76:

247/0.76:

= 325

So, the regular price was $325

ANSWER ASAP IM BEING TIMED
IF I GET AN A ON THIS I WILL DO ANOTHER POINT FREE DROP, PLEASE SHOW YOUR WORK
The lengths of three sides of a quadrilateral are shown below:

Side 1: 1y2 + 3y − 6

Side 2: 4y − 7 + 2y2

Side 3: 3y2 − 8 + 5y

The perimeter of the quadrilateral is 8y3 − 2y2 + 4y − 26.

Part A: What is the total length of sides 1, 2, and 3 of the quadrilateral? (4 points)

Part B: What is the length of the fourth side of the quadrilateral? (4 points)

Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer. (2 points)

Answers

Answer:

Part A

(1y^2+3y-6)+(4y-7+2y^2)+(3y^2-8+5y)

6y^2+12y-21

if you subtract 1/2 from a number and multiply the result by 1/2 you get 1/8. What is the no.

Answers

Step-by-step explanation:

1/6

1/6- 1/2 = 1/4

1/4*1/2= 1/8

The number is 3/4


Step by step

1/(N-1/2)•1/2=1/8
2/N-1/2=1/8 divided 1/2 But the 1/2 in the other side by dividing
3/ N-1/2=1/4
4/N=1/4+1/2
5/N=3/4
If you check
3/4-1/2=1/4
1/4•1/2=1/8


Suppose you buy a home and finance $275,000 at $2,223.17 per month for 30 years. What is the amount of interest paid? (Round your answer to the nearest cent.)

Answers

Answer:  $525,341.20

Explanation:

30 years = 30*12 = 360 months

If the monthly payment is $2,223.17 for 360 months, then you'll pay back a total of 2223.17*360 = 800,341.20 dollars overall.

Subtract off the amount financed, or amount loaned, to get the total interest.

800,341.20 - 275,000 = 525,341.20 is the amount of interest paid (in dollars).

This works because effectively, the total amount paid back consists of principal + interest. The principal is the amount the bank loans you.

So we could rephrase that last equation into saying

principal + interest = 275,000 + 525,341.20 = 800,341.20 = total amount paid back.

which of the following function shows the absolute value parent function FX=lxl shifted up

Answers

Answer:

The answer is C.

as for C . the value of f(x) increases by 7 and so the graph goes up by units 7.

OR

g(x) = |x| + 7

we know that |x| is f(x), so :-

g(x) = f(x) + 7

and since f(x) is plot on y- axis the graph climbs the y axis by 7 units

*The graph shifts right or left for the other functions*

The probability that a 38-year-old white male will live another year is .99813. What premium would an insurance company charge to break even on a one-year $1 million term life insurance policy

Answers

Answer:

The insurance company should charge $1,873.5.

Step-by-step explanation:

Expected earnings:

1 - 0.99813 = 0.00187 probability of the company losing $1 million(if the client dies).

0.99813 probability of the company earning x(price of the insurance).

What premium would an insurance company charge to break even on a one-year $1 million term life insurance policy?

Break even means that the earnings are 0, so:

[tex]0.99813x - 0.00187(1000000) = 0[/tex]

[tex]0.99813x = 0.00187(1000000)[/tex]

[tex]x = \frac{0.00187(1000000)}{0.99813}[/tex]

[tex]x = 1873.5[/tex]

The insurance company should charge $1,873.5.

The greatest number of elements possible in

Answers

Answer:

4

9

Step-by-step explanation:

If X has 5 elements, and Y has 4 elements, and all 4 of Y's elements are the same as 4 of X's elements, then the intersection of the sets has 4 elements.

If X has 5 elements and Y has 4 elements, and they are all different, then the union of the sets has 9 elements.

Answer:

4

9

Please look at the included picture, show me your work and please include a good explanation. It would really help me out here.

Answers

These are indeed equivalent, and this identity is one of DeMorgan's laws.

The 6th column is the negation of the 5th column. For example, the first row says

not p or q

is true (T), so the negation would be false (F). The 5th column reads {T, F, T, T}, so the next column should be {F, T, F, F}.

Then in the 7th/last column, you are checking the truth value of the statement

p and not q

For example, in the first row, both p and q are true (T). This means (not q) is false, so (p and not q) is false (F). The last column should end up reading {F, T, F, F}, same as the previous column.

Lim x>0 (x(e^3x - 1)/(2 - 2cosx))

Answers

Evaluating the limand directly at x = 0 yields the indeterminate form 0/0. If L'Hopital's rule is known to you, you can compute the limit by applying it twice:

[tex]\displaystyle\lim_{x\to0}\frac{x\left(e^{3x}-1\right)}{2-2\cos(x)} = \lim_{x\to0}\frac{3xe^{3x}+e^{3x}-1}{2\sin(x)} \\\\\\ = \lim_{x\to0}\frac{9xe^{3x}+6e^{3x}}{2\cos(x)} = \frac62=\boxed{3}[/tex]

You’re making 40 servings of English custard. Each serving is 250 ml. The following recipe yields 2 L.

Calculate how much of each ingredient you will need to make enough servings of the custard.

Milk 2 L

Vanilla essence 4 ml

Sugar 200 g

Egg yolks 20

Answers

Answer:

Milk   10 L

Vanilla essence  = 20 ml

Sugar   = 1kg

Egg yolks   100 yolks

Step-by-step explanation:

2l/250ml = 8 servings per recipe ,

40 servings/8 = 5 "batches"

Milk 2 L * 5 = 10 L

Vanilla essence 4 ml * 5 = 20 ml

Sugar 200 g * 5  = 1000g = 1kg

Egg yolks 20 * 5 = 100 yolks

Two linear equations are shown in the graph.
#Brainliest award
What are the coordinates of the point where the two lines intersect?
A. (–2, 3)
B. (3, 3)
C. (3, 0)
D. (–3, 3)

Answers

Answer:

I am taking this graph because this question looked similar to this one.

Step-by-step explanation:

Answer should be B.

The intersection point is (3,3)

Is the collection og rall " student in set ? why ? class7​

Answers

Answer:

in secret

Step-by-step explanation:

correct answer is in a secret

The cone and the cylinder below have equal surface area. O A. True O B. False ​

Answers

Answer:

the answer is false

Step-by-step explanation:

comment if you want explanation

Answer:

True

Step-by-step explanation:

When using the formulas to find the surface area, both have equal surface area

What is the value of 3 minus (negative 2)?

A number line going from negative 5 to positive 5.

Answers

Answer:

5

Step-by-step explanation:

3-(-2) will become positive 5. so number line will go towards positive 5.

Find the distance between the two points in simplest radical form. (-6,1) and (−8,−4)

Answers

Answer: 5

Step-by-step explanation: I think it is 5

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