A population proportion is 0.61. Suppose a random sample of 658 items is sampled randomly from this population

a. What is the probability that the sample proportion is greater than 0.63?

b. What is the probability that the sample proportion is between 0.60 and 0.66?

c. What is the probability that the sample proportion is greater than 0.592

d. What is the probability that the sample proportion is between 0.57 and 0.60?

e. What is the probability that the sample proportion is less than 0.51?

Answers

Answer 1

Answer:

Explained below.

Step-by-step explanation:

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

[tex]\mu_{\hat p}=p[/tex]

The standard deviation of this sampling distribution of sample proportion is:

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

A random sample of n = 658 items is sampled randomly from this population.

As the sample size is large, i.e. n = 658 > 30, the Central limit theorem can be applied to approximate the sampling distribution of sample proportion by a Normal distribution.

Compute the mean and standard deviation as follows:

[tex]\mu_{\hat p}=0.61\\\\\sigma_{\hat p}=\sqrt{\frac{0.61(1-0.61)}{658}}=0.019[/tex]

(a)

Compute the probability that the sample proportion is greater than 0.63 as follows:

[tex]P(\hat p>0.63)=P(\frac{\hat p-\mu_{\hat p}}{\sigma_{\hat p}}>\frac{0.63-0.61}{0.019})\\\\=P(Z>1.05)\\\\=1-P(Z<1.05)\\\\=1-0.85314\\\\=0.14686\\\\\approx 0.1469[/tex]

(b)

Compute the probability that the sample proportion is between 0.60 and 0.66 as follows:

[tex]P(0.60<\hat p<0.66)=P(\frac{0.60-0.61}{0.019}<\frac{\hat p-\mu_{\hat p}}{\sigma_{\hat p}}<\frac{0.66-0.61}{0.019})\\\\=P(-0.53<Z<2.63)\\\\=P(Z<2.63)-P(Z<-0.53)\\\\=0.99573-0.29806\\\\=0.69767\\\\\approx 0.6977[/tex]

(c)

Compute the probability that the sample proportion is greater than 0.592 as follows:

[tex]P(\hat p>0.592)=P(\frac{\hat p-\mu_{\hat p}}{\sigma_{\hat p}}>\frac{0.592-0.61}{0.019})\\\\=P(Z>-0.95)\\\\=P(Z<0.95)\\\\=0.82894\\\\\approx 0.8289[/tex]

(d)

Compute the probability that the sample proportion is between 0.57 and 0.60 as follows:

[tex]P(0.57<\hat p<0.60)=P(\frac{0.57-0.61}{0.019}<\frac{\hat p-\mu_{\hat p}}{\sigma_{\hat p}}<\frac{0.60-0.61}{0.019})\\\\=P(-2.11<Z<-0.53)\\\\=P(Z<-0.53)-P(Z<-2.11)\\\\=0.29806-0.01743\\\\=0.28063\\\\\approx 0.2806[/tex]

(e)

Compute the probability that the sample proportion is less than 0.51 as follows:

[tex]P(\hat p<0.51)=P(\frac{\hat p-\mu_{\hat p}}{\sigma_{\hat p}}<\frac{0.51-0.61}{0.019})\\\\=P(Z<-5.26)\\\\=0[/tex]


Related Questions

I help to solve this problem by adding integers -2+(-4)

Answers

Answer:

-6

Step-by-step explanation:

-2 + (-4)

-2 - 4

-6

Answer:

-6 is the answer

Step-by-step explanation:

Solve.
2(z - 10) = -4

Answers

Answer:

z=8

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

2(z−10)=−4

(2)(z)+(2)(−10)=−4(Distribute)

2z+−20=−4

2z−20=−4

Step 2: Add 20 to both sides.

2z−20+20=−4+20

2z=16

Step 3: Divide both sides by 2.

2z2=162

z=8

find the values of x and y

Answers

Answer:

x = 90

y = 43

Step-by-step explanation:

[tex] In\: \triangle ABC\\

AB = AC.... (given)

\therefore m\angle ABC = m\angle ACB\\[/tex] (Property of isosceles triangle)

[tex] \because m\angle ACB = 47\degree \\

\therefore m\angle ABC = 47\degree \\

2y\degree + 47\degree+47\degree = 180\degree \\

2y\degree + 94\degree= 180\degree \\

2y\degree = 180\degree - 94\degree \\

2y\degree = 86\degree \\\\

y = \frac{86\degree}{2} \\\\

y\degree = 43\degree \\\\

\huge \purple {\boxed {y = 43}} \\\\[/tex]

x° + y° + 47°=180°

x° + 43° + 47°=180°

x ° + 90° = 180°

x ° = 180° - 90°

x° = 90°

x = 90

In the diagram below, DE is parallel to XY. What is the value of y?

Answers

Answer:

Option A . 122°

.............

Answer: A) 122

Explanation:

Alternate exterior angles are congruent when we have parallel lines like this.

You can use their vertical angle counterparts to then use the alternate interior angles if you want.

Find the instantaneous rate of change of the function f(x)=3x^2 as x approaches 3.

Answers

Answer:

The instantaneous rate of change as x approaches 3 is 18.

Step-by-step explanation:

From Differential Calculus and Geometry we remember that instantaneous rate of change of the function is represented by a tangent line, whose slope is determined by the first derivative of the curve. Let [tex]f(x) = 3\cdot x^{2}[/tex], the instantaneous rate of change of the function when x approaches 3 is deducted from the definition of derivative:

[tex]f'(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}[/tex] (1)

[tex]f'(x) = \lim_{h\to 0} \frac{3\cdot (x+h)^{2}-3\cdot x^{2}}{h}[/tex]

[tex]f'(x) = \lim_{h\to 0} \frac{3\cdot (x^{2}+2\cdot x\cdot h +h^{2})-3\cdot x^{2}}{h}[/tex]

[tex]f'(x) = \lim_{h\to 0} \frac{3\cdot x^{2}+6\cdot x\cdot h+3\cdot h^{2}-3\cdot x^{2}}{h}[/tex]

[tex]f'(x) = \lim_{h\to 0} \frac{6\cdot x\cdot h +3\cdot h^{2}}{h}[/tex]

[tex]f'(x) = \lim _{h\to 0} (6\cdot x+3\cdot h)[/tex]

[tex]f'(x) = 6\cdot x \cdot \lim_{h\to 0} 1 + 3\cdot \lim_{h\to 0} h[/tex]

[tex]f'(x) = 6\cdot x[/tex] (2)

If we know that [tex]x = 3[/tex], then the instantaneous rate of change as x approaches 3 is:

[tex]f'(3) = 6\cdot (3)[/tex]

[tex]f'(3) = 18[/tex]

The instantaneous rate of change as x approaches 3 is 18.

How many integers are between - 6,01 and 7.75?

13

14

15

16

Answers

Answer:

14 integers

Step-by-step explanation:

Given

[tex]Range: -6.01\ to\ 7.75[/tex]

Required

Determine the number of integers

Integers implies numbers without decimals; it could be positive or negative or 0.

So, within the range: the integers are:

[tex]-6, -5, -4,-3,-2,-1,0,1,2,3,4,5,6,7[/tex]

Notice that the above numbers are integers within the given range.

By counting them, we get the required number of integers.

[tex]Numbers = 14[/tex]

Hence, there are 14 integers

At the grocery store, sliced turkey deli meat is on sale for $11 for 2 pounds. a. What is the cost per pound of sliced turkey deli meat? b. Write an equation to represent the cost "y" of sliced turkey deli meat measured in "x" pounds. *

Answers

Answer:

- $5.5 per pound

- [tex]y = 5.5x[/tex]

Step-by-step explanation:

Given

$11 for 2 pounds

Solving (a): Cost per pound

This is calculated by dividing $11 by 2 pounds

[tex]Cost\ per\ pound = \frac{\$11}{2\ lb}[/tex]

[tex]Cost\ per\ pound = \$5.5/\ lb[/tex]

Hence, the cost per pound is $5.5 per pound

Solving (b): Represent as an equation.

If 1 pound costs $5.5 (as shown in (a))

Then

x pounds costs $5.5 * x

[tex]Cost = 5.5 * x[/tex]

[tex]Cost = 5.5x[/tex]

This cost is represented with y

[tex]y = 5.5x[/tex]

What is the solution to this system of linear equations?
2x + 3y = 3
7x - 3y = 24
O (2,7)
(3,-21)
(3,-1)
O (9,0)

Answers

Answer:

(3,-1)

Hope this helps! :)

Answer:

C

Step-by-step explanation:

just got it right on edge

Can anyone help me determine the next terms in these sequences?
6, 8, ?, 16, 24, 28,...
1000, 999, 996, 991, 984,...
7, 9, 13, 17, ?, 29,...
8, 11, 29, 51, 125, ?, 293,...
9, 11, 30, 51, 126, ?, 294,...
102532, 112433, 122334,...

Answers

Answer:

132235

Step-by-step explanation:

Sharon paid $78 sales tax on a new camera. If the sales tax is 6.5%, what was the cost of the camera?

Answers

Answer:

$1200

Step-by-step explanation:

$1200

Step-by-step explanation:

78 = 6.5%

This means that if you divide 78 by 6.5, you get the equivalent of 1% of the price:

78 ÷ 6.5 = 12

So 1% = 12

Now simply multiply this by 100 to get the full answer:

12 x 100 = 1200

So the camera cost $1200!

Answer:

$1,200

Step-by-step explanation:

78 divided by 6.5=12

With percents you have to multiply to get out of 100 so:

12x100=1,200

78 divided by 6.5%=1,200

-SunflowerJada

(3^8x 2^-5x 9^0)^-2x (2^-2/3^3)^4x 3^28 PLS HELP

Answers

Answer:

(3^8x 2^-5x 9^0)^-2x (2^-2/3^3)^4x 3^28 =4

i hope this is correct

Step-by-step explanation:

ASAP
3(– 2а - 4) + За

Answers

Answer:

3a -12

Step-by-step explanation:

3(– 2а - 4) + За  →  -6a - 12 + 3a  →  -3a -12

Help me out here please....

Answers

4 because when it’s all added up

FIRST TO HELP IS BRAINLIEST

Answers

Answer:

(0,2)

Step-by-step explanation:

find the GCF of the ​

Answers

Answer:

6x

Step-by-step explanation:

24 and 30 share a GCF of 6. x^2 and x^2y share a GCF of x as we do not know what the value of y is.

Answer:

6xxxxxxxxxxxxxxxx with one x

Read the description of f below, and then use the drop-down menus to complete an
explanation of why f is or is not a function,
f relates each student in Mr. Well's history class to their score on a final exam.

Answers

Answer:

because a function always gives a determined answer from what was placed into the domain, this is not a function. what is put into the domain (students) may not get the same result through f.

Answer: 1. the students 2. the final exams 3. is- domain- one- range   brainliest plzz??

Find the GCF for the following list.
108. 100

Answers

Answer:

Step-by-step explanation:

2

Answer:

4

Step-by-step explanation:

108 divided by 4 = 27

100 divided by 4 = 25

Good luck!

Jason is buying a car, and he wants to pay for it in 48 monthly installments. If the total cost of the car is $9,300, how much would Jason have to pay each month?
$500 per month
$195 per month
$193.75 per month
$193.50 per month

Answers

the answer is 193.75 per month

a bag of mixed nuts contains almonds and hazelnuts there are (6x + 13) nuts in particular bag

Answers

Answer:

99=00-41+69=6969

Step-by-step explanation:

Which of these quadrilaterals have opposite sides that are parallel? Name these quadrilateral

Answers

Answer:

square,rectangle,rhombus,paralellagram

Step-by-step explanation:

Zoey invested $230 in an account paying an interest rate of 6.3% compounded daily.
Assuming no deposits or withdrawals are made, how much money, to the nearest
hundred dollars, would be in the account after 12 years?

Answers

Answer:

A ≈ $500

General Formulas and Concepts:

Pre-Alg

Order of Operations: BPEMDAS

Algebra I

Compounded Interest Rate: A = P(1 + r/n)ⁿˣ

A is final amountP is initial (principle) amountr is raten is number of compoundsx is number of years

Step-by-step explanation:

Step 1: Define

P = 230

r = 0.063

n = 365

x = 12

Step 2: Solve for A

Substitute:                    A = 230(1 + 0.063/365)³⁶⁵⁽¹²⁾Divide:                          A = 230(1 + 0.000173)³⁶⁵⁽¹²⁾Multiply:                        A = 230(1 + 0.000173)⁴³⁸⁰Add:                              A = 230(1.00017)⁴³⁸⁰Exponents:                   A = 230(2.1296)Multiply:                        A = 489.808

25% of 88 is what number?
Math

Answers

Answer: 22

What is 25 percent (calculated percentage %) of number 88? Answer: 22.

Answer:

25% of 88 is 22

88 times .25 because it is a decimal

Write the fraction 4/6 as a decimal. Round to the nearest hundredth

Answers

0.67 hope this helped. Please give Brainly

The value of solution after divide in form of decimal is,

⇒ 0.67

We have to given that,

To write the fraction 4/6 as a decimal.

We can simplify the fraction and then divide,

⇒ 4 /6

⇒ 2 / 3

⇒ 0.67

Rounded to nearest hundredth.

Therefore, The value of solution after divide in form of decimal is,

⇒ 0.67

Learn more about the divide visit:

https://brainly.com/question/28119824

#SPJ6

A submarine descends 1/120 mile every minute. Write a product of three or more rational numbers to represent the change in the submarines elevation after 3 hours. Then find the value of the product and explain what it represents.

Answers

9514 1404 393

Answer:

  (1/120 mile/min)(60 min/h)(3 h)

  1.5 mile

  the increase in depth after 3 hours

Step-by-step explanation:

The rate is given in terms of miles per minute. To find the elevation after 3 hours, we need a conversion from minutes to hours. One possible product is ...

  (1/120 mile/min)(60 min/h)(3 h)

The value of this product is ...

  (1·60·3)/(120·1·1) mile = 1.5 mile

The value represents the increase in depth after 3 hours.

A random sample of a specific brand of snack bar is tested for calorie count, with the following results:

149 145 140 160 149 153 131 134 153

Assume the population standard deviation is ı = 24 and that the population is approximately normal. Construct a 95% confidence interval for the calorie count of the snack bars.

Answers

Answer:

iddiduududjdhdhdjdhdjr

6. Grandma's favorite muffin recipe uses 1 cups of
flour for one batch of 12 muffins. Solve each of the
following problems and determine whether it is
a “how many groups?" or a “how many in one group?"
type of division problem. Give an exact answer to
each problem using a common fraction or
a mixed number.
(a) How many cups of flour are in 1 muffin?
(b) How many muffins does 1 cup of flour make?
(Assume that you can make partial muffins).
(C) If you have 4 cups of flour, then how many
batches of muffins can you make? (Assume
that you can make partial batches).

Answers

Answer:

im to hungry now to answer

Step-by-step explanation:

How do you do this question?

Answers

Step-by-step explanation:

f(x) = sin(x), a = π/6, n = 4

Find the derivatives.

f⁽⁰⁾(π/6) = sin(π/6) = ½

f⁽¹⁾(π/6) = cos(π/6) = ½√3

f⁽²⁾(π/6) = -sin(π/6) = -½

f⁽³⁾(π/6) = -cos(π/6) = -½√3

f⁽⁴⁾(π/6) = sin(π/6) = ½

T₄(x) = ½ (x − π/6)⁰ / 0! + ½√3 (x − π/6)¹ / 1! − ½ (x − π/6)² / 2! − ½√3 (x − π/6)³ / 3! + ½ (x − π/6)⁴ / 4!

T₄(x) = ½ + ½√3 (x − π/6) − ¼ (x − π/6)² − ¹/₁₂√3 (x − π/6)³ + ¹/₄₈ (x − π/6)⁴

Find the fifth derivative.

f⁽⁵⁾(x) = cos(x)

So the next term of the series would be:

cos(z) (x − π/6)⁵ / 5!

For 0 ≤ z ≤ π/3,│f⁽⁵⁾(x)│is a maximum at z = 0.  Therefore:

│R₄(x)│≤ │cos(0) (0 − π/6)⁵ / 5!│

│R₄(x)│≤ 0.000328

│R₄(x)│is always positive, so we can ignore the bottom two graphs.  The top right graph has a y-intercept of approximately 0.0003, so that is the correct graph.

Paulina ran 6.2 miles last week and 10.95 miles this week.
How many miles did she run in all?

Answers

Answer: 17.15

Step-by-step explanation:

6.2+10.95=17.15

Answer:

gghhhhfhfuubf

Step-by-step explanation:

The first step to solve the equation x/4-3/4=16 is shown below

Answers

Answer:

i think it is A because that seems like the one making the most sense

Step-by-step explanation:

The following are the ages (years) of 5 people in a room: 22, 13, 17, 15, 17 A person enters the room. The mean age of the 6 people is now 17. What is the age of the person who entered the room?

Answers

Answer:

the 6th man's age is 58!

Step-by-step explanation:

First you have to find the mean of 22, 13, 17, 16, and 17, by first adding 22, 13, 17, 16, and 17 to get 85. Because mean is the numbers added up divided by the total amount of numbers, there are 5 numbers and then you have to divided 85 by 5.

After you get the mean of these numbers, find the other number which will level the mean to 17.

yes this was a lame explanation sorry i'm only in 7th grade and this is all new to me

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