MATHEMATICS COLLEGE

Consider random samples of size 40 from a population with proportion 0.15. (a) Find the standard error of the distribution of sample proportions.
Round your answer for the standard error to three decimal places.
mean=
standard error=_
(b) Is the sample size large enough for the Central Limit Theorem to apply?
1. Yes
2. No

Answers

Answer 1

Answer:

The standard error of the distribution of sample proportions is 0.056 and mean is 0.15.

Yes, the sample size is enough for the Central Limit Theorem to apply.

(a). Given that, size of sample, $n=40$

Proportion, $p=0.15$

In the distribution of sample proportions, mean $\mu=p$

and, standard error = $\sqrt{(p(1-p))/(n) }$

So, mean $\mu=0.15$

Standard error = $\sqrt{(0.15(1-0.15))/(40) }=0.056$

(b). The Central Limit Theorem applies if np > 5 .

$np=40*0.15=6>5$

Thus, the Central Limit Theorem is applied.

Learn more:

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Answer 2

Answer:

Answer:

a) The mean is 0.15 and the standard error is 0.056.

b) 1. Yes

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = (\sigma)/(√(n))$ .

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

For proportions p, in samples of size n, the mean is $\mu = p$ and the standard error is $s = \sqrt{(p(1-p))/(n)}$ . The Central Limit Theorem applies is np > 5 and np(1-p)>5.

In this question:

$n = 40, p = 0.15$

(a) Find the mean and the standard error of the distribution of sample proportions.

$\mu = 0.15, s = \sqrt{(0.15*0.85)/(40)} = 0.056$

So the mean is 0.15 and the standard error is 0.056.

(b) Is the sample size large enough for the Central Limit Theorem to apply?

np = 40*0.15 = 6 > 5

np(1-p) = 40*0.15*0.85 = 5.1>5

So yes

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In one city, the ratio of households with pets tohouseholds without pets is 30 to 29. If 20,735 households
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Answers

Answer:

40,779

Step-by-step explanation:

i took the k12 test

01) What is the perimeter of shape B?
2) Which shape's perimeter is less? Shape A or shape D.
3) Area of which shape is more?
4) Area of which shapes are equal?
5) Which shape has equal perimeter and area?
TA)
(B)
(c)
(D)

Answers

Answer:

whichshape's permeteris less shape A or D shape.

Answer:

ask google assistaint then if you dont get it go f yourself like u did to me

Step-by-step explanation:

What is the solution to the following inequality X/-2 > 5

Answers

Answer:

x < -10

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Step-by-step explanation:

Step 1: Define

Identify

x/-2 > 5

Step 2: Solve for x

[Multiplication Property of Equality] Multiply -2 on both sides: x < -10

$\large {\mathsf {\red{\underbrace {\overbrace{\blue{ {\pink}{Answєr}}}}}}} \:$

x > - 10

$\large \mathtt \green{Step-by-step \: explanation : }$

$\small \sf (x)/( - 2) > 5 \n$

Solve forx

$\small \sf (x)/( - 2) > 5 \n$

common denominator is 2

$\small \sf ➪ (2x)/( - 2) >2 * 5 \n$

$\small \sf ➪ \frac{ \cancel{2}x}{ - \cancel{ 2}} >2 * 5 \n$

➪ - x > 2 × 5

➪ - x > 10

multiply by - 1

➪ - x × - 1 > 10 × - 1

x > - 10

A particular concentration of a chemical found in polluted water has been found to be lethal to 40% of the crayfish that are exposed to the concentration for 24 hours. 22 crayfish are placed in a tank containing this concentration of chemical in the water. (a) What is the probability that 13 or 17 survive?
(b) What is the probability that at least 17 survive?
(c) What is the probability that at most 16 survive?
(d) What number of crayfish are expected to survive?
(e) What is the variance in the number of crayfish that are expected to survive? No actual crayfish were harmed in the making of this question.

Answers

Answer:

a) $P(X=13)=(24C13)(0.4)^(13) (1-0.4)^(24-13)=0.0608$

$P(X=17)=(24C17)(0.4)^(17) (1-0.4)^(24-17)=0.0017$

$P(X=13 U X=17) = 0.0608+0.0017=0.0624$

b) $P(X \geq 17)=0.000427$

c) $P(X \geq 16)= 1-0.000427=0.9996$

d) $E(X)= np = 22*0.4=8.8$

e) $Var(X) = np(1-p)= 22*0.4*(1-0,4)=5.28$

Step-by-step explanation:

1) Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

2) Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=24, p=0.4)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^(n-x)$

Where (nCx) means combinatory and it's given by this formula:

$nCx=(n!)/((n-x)! x!)$

3) Part a

$P(X=13)=(22C13)(0.4)^(13) (1-0.4)^(22-13)=0.0336$

$P(X=17)=(22C17)(0.4)^(17) (1-0.4)^(22-17)=0.00035$

$P(X=13 U X=17) = 0.0336+0.00035=0.0340$

4) Part b

$P(X \geq 17)=P(X=17)+P(X=18)+P(X=19)+P(X=20)+P(X=21)+P(X=22)$

$P(X=17)=(22C17)(0.4)^(17) (1-0.4)^(22-17)=0.00035$

$P(X=18)=(22C18)(0.4)^(18) (1-0.4)^(22-18)=0.0000651$

$P(X=19)=(22C19)(0.4)^(19) (1-0.4)^(22-19)=0.00000914$

$P(X=20)=(22C20)(0.4)^(20) (1-0.4)^(22-20)=0.000000914$

$P(X=21)=(22C21)(0.4)^(21) (1-0.4)^(22-21)=5.81x10^(-8)$

$P(X=22)=(22C22)(0.4)^(22) (1-0.4)^(22-22)=1.76x10^(-9)$

$P(X \geq 17)=0.000427$

5) Part c

$P(X \leq 16)=1-P(X>16)=1-P(X\geq 17) = 1-[P(X=17)+P(X=18)+P(X=19)+P(X=20)+P(X=21)+P(X=22)]$

$P(X \geq 16)= 1-0.000427=0.9996$

6) Part d

The expected value is:

$E(X)= np = 22*0.4=8.8$

7) Part e

The variance is given by:

$Var(X) = np(1-p)= 22*0.4*(1-0,4)=5.28$

HELP PLS MATH HELP ASAP CORRECT ANSWER ONLY PLS

Answers

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

3(2)+2=8

3(3)+2=11

3(4)+2=14

3(5)+2=17

3(6)+2=20

Sum=70

Two sides of an obtuse triangle measure 10 inches and 15 inches. The length of longest side is unknown.What is the smallest possible whole-number length of the unknown side?

Answers

Answer:

The smallest possible whole-number length of the unknown side is $19\ inches$

Step-by-step explanation:

we know that

The triangle inequality theorem, states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side

Let

x-----> the length of longest side

Applying the triangle inequality theorem

case A)

$10+15 > x$

$25 > x$

Rewrite

$x< 25$

case B)

$10+x > 15$

$x > 15-10$

$x> 5$

The solution of the third side is the interval-------> $(5,25)$

but remember that

In an obtuse triangle

$x^(2) > a^(2) +b^(2)$

$x^(2) > 15^(2) +10^(2)$

$x > 18.03\ inches$

Round to a whole number

$x= 19\ inches$

10^2 (10 squared) + 15^2 = C^2
100+225=c^2
325=c^2
√325
√25⋅13
√ 25 ⋅√13
5√ 13√325≈18.027756377319946
The whole number would be 5√ 13
It's the converse of the Pythagorean theorem.

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