The variance of the scores on a skill evaluation test is 143,641 with a mean of 1517 points. If 343 tests are sampled, what is the probability that the mean of the sample would differ from the population mean by less than 36 points

Answer:

6.7%

Step-by-step explanation:

Answer:

0.9452 = 94.52% probability that more than 3 adults in the sample prefer saving over spending

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they prefer saving over spending, or they do not. The answers for each adult are independent, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

According to a Gallup poll, 60% of American adults prefer saving over spending.

This means that [tex]p = 0.6[/tex]

Sample of 10 American adults

This means that [tex]n = 10[/tex]

What is the probability that more than 3 adults in the sample prefer saving over spending?

This is:

[tex]P(X > 3) = 1 - P(X \leq 3)[/tex]

In which

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{10,0}.(0.6)^{0}.(0.4)^{10} = 0.0001[/tex]

[tex]P(X = 1) = C_{10,1}.(0.6)^{1}.(0.4)^{9} = 0.0016[/tex]

[tex]P(X = 2) = C_{10,2}.(0.6)^{2}.(0.4)^{8} = 0.0106[/tex]

[tex]P(X = 3) = C_{10,3}.(0.6)^{3}.(0.4)^{7} = 0.0425[/tex]

Then

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0001 + 0.0016 + 0.0106 + 0.0425 = 0.0548[/tex]

[tex]P(X > 3) = 1 - P(X \leq 3) = 1 - 0.0548 = 0.9452[/tex]

0.9452 = 94.52% probability that more than 3 adults in the sample prefer saving over spending

Answer:

The probability is 1/2500. (1/50)*(1/50)

Step-by-step explanation:

y=3× + 7 , y=×- 9 , 3×- 9 , 3×- y= 1 , 7× + 2y = 37.

Answer:

TS = 12.7

Step-by-step explanation:

From the question given above, the following data were obtained:

QR = 9

QP = 6

TU = 19

TS =?

Since the triangles are SIMILAR, then,

QR / TU = QP / TS

With the above equation, we can obtain the value of TS as follow:

QR = 9

QP = 6

TU = 19

TS =?

QR / TU = QP / TS

9 / 19 = 6 / TS

Cross multiply

9 × TS = 19 × 6

9 × TS = 114

Divide both side by 9

TS = 114 / 9

TS = 12.7

9514 1404 393

Answer:

Step-by-step explanation:

Let 'a' represent the number of pounds of Arabian Mocha in the mix. Then the number of pounds of Costa Rican blend is (100-a). The cost of the mix will be ...

  9.10(100 -a) +13.10(a) = 11.58(100)

  4a = 248 . . . . . . . . . . . . . collect terms, subtract 910

  a = 62 . . . . . . . . . . . . divide by 4

62 pounds of Arabian Mocha and 38 pounds of Costa Rican blend should be mixed.

Answer:

[tex]c = \frac{1}{12}[/tex]

The mean of the distribution is 0.25.

The variance of the distribution is of 0.6875.

Step-by-step explanation:

Probability density function:

For it to be a probability function, the sum of the probabilities must be 1. The probabilities are 3c, 3c and 6c, so:

[tex]3c + 3c + 6c = 1[/tex]

[tex]12c = 1[/tex]

[tex]c = \frac{1}{12}[/tex]

So the probability distribution is:

[tex]P(X = -1) = 3c = 3\frac{1}{12} = \frac{1}{4} = 0.25[/tex]

[tex]P(X = 0) = 3c = 3\frac{1}{12} = \frac{1}{4} = 0.25[/tex]

[tex]P(X = 1) = 6c = 6\frac{1}{12} = \frac{1}{2} = 0.5[/tex]

Mean:

Sum of each outcome multiplied by its probability. So

[tex]E(X) = -1(0.25) + 0(0.25) + 1(0.5) = -0.25 + 0.5 = 0.25[/tex]

The mean of the distribution is 0.25.

Variance:

Sum of the difference squared between each value and the mean, multiplied by its probability. So

[tex]V^2(X) = 0.25(-1-0.25)^2 + 0.25(0 - 0.25)^2 + 0.5(1 - 0.25)^2 = 0.6875[/tex]

The variance of the distribution is of 0.6875.

Answer:

irrational numbers

Step-by-step explanation:

An irrational number is a number that cannot be expressed as a fraction p/q for any integers p and q.

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Irrational Number

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Answer:

The answer is "0.18"

Step-by-step explanation:

[tex]10\% \ of \ 50= 5 \text{are left handed}\\\\45\ \text{are right handed}\\\\[/tex]

If the probability exactly 4 were heft handed

 [tex]=^{50}_{C_4}\times (\frac{5}{50})^4 \times (\frac{45}{50})^{4b}\\\\=^{50}_{C_4} \times (0.1)^4 \times (0.9)^{4b}\\\\=230300 \times (0.1)^4 \times (0.9)^{4b}\\\\=0.181 \approx 0.18[/tex]

Answer:

74 inches

Step-by-step explanation:

1 foot is 12 inches, so 6 x 12 = 72, and just add the other 2 inches to get 74 inches.

Answer:

74 inches.

Step-by-step explanation:

Each foot has 12 inches, so multiply 6 by 12 to get 72 inches. Then add the remaining two inches to get a total of 74 inches.

Answer:

$ 1943

Step-by-step explanation:

You two congruent trapezoids.

Find the area of one and multiply by 2.

A = [tex]\frac{base_{1} + base_{2} }{2}[/tex] x  h

  = [tex]\frac{28+39}{2}[/tex] x 14.5

  = [tex]\frac{67}{2}[/tex] x 14.5

  = 33.5 x 14.5

  = 485.75

  = 485.75 x 2 (Two trapezoids)

  = 971.50

  = 971.50 x 2 (two dollars a square foot)

  = 1943.00

Answer:

y = 5x + 1

Step-by-step explanation:

Given the coordinate points (0,1) and (5,0)

First, get the slope

Slope m =(0-1)/5-0

m = -1/5

Since the required line is perpendicular, then the required slope is;

M = -1/(-1/5)

M = 5

Since 1the y intecept id (0,1) i.e. 1

Required equation is y = mx+b

y = 5x + 1

This gives the required equation

Note that the coordinate (0,1) was used instead os (0,0)

Answer:

(a) 74553

(b) 172120

(c) 234802

Step-by-step explanation:

Given

[tex]y = \frac{340110}{1 + 377e^{-0.259t}}[/tex]

Solving (a): 1998

Year 1998 means that:

[tex]t =1998 - 1980[/tex]

[tex]t =18[/tex]

So, we have:

[tex]y = \frac{340110}{1 + 377e^{-0.259*18}}[/tex]

[tex]y = \frac{340110}{1 + 377e^{-4.662}}[/tex]

[tex]y = \frac{340110}{1 + 3.562}[/tex]

[tex]y = \frac{340110}{4.562}[/tex]

[tex]y = 74553[/tex] --- approximated

Solving (b): 2003

Year 2003 means that:

[tex]t = 2003 - 1980[/tex]

[tex]t =23[/tex]

So, we have:

[tex]y = \frac{340110}{1 + 377e^{-0.259*23}}[/tex]

[tex]y = \frac{340110}{1 + 377e^{-5.957}}[/tex]

[tex]y = \frac{340110}{1 + 0.976}[/tex]

[tex]y = \frac{340110}{1.976}[/tex]

[tex]y = 172120[/tex] --- approximated

Solving (c): 2006

Year 2006 means that:

[tex]t = 2006 - 1980[/tex]

[tex]t =26[/tex]

So, we have:

[tex]y = \frac{340110}{1 + 377e^{-0.259*26}}[/tex]

[tex]y = \frac{340110}{1 + 377e^{-6.734}}[/tex]

[tex]y = \frac{340110}{1 + 0.4485}[/tex]

[tex]y = \frac{340110}{1.4485}[/tex]

[tex]y = 234802[/tex] --- approximated

Answer:

[tex] \large{ \tt{❃ \: S \: O \: L \: U \: T \: I \: O \: N : }}[/tex]

[tex] \large{ \tt{⇢m \: \angle \: GHI= m \: \angle \: GHQ + m \: \angle \: QHI}}[/tex]

[tex] \large{ \tt{➝14x + 6 = 3x - 3 + 130 \degree}}[/tex]

[tex] \large{ \tt{➝14x + 6 = 3x + 127}}[/tex]

[tex] \large{ \tt{➝ \: 14x - 3x = 127 - 6}}[/tex]

[tex] \large{ \tt{➝ \: 11x = 121}}[/tex]

[tex] \large{ \tt{➝ \: x = \frac{121}{11} }}[/tex]

[tex] \large{ \tt{➝ \: x = 11}}[/tex]

[tex] \large{ \tt{✣ \: REPLACING \: VALUE}} : [/tex]

[tex] \large{ \tt{✺ \: m \: \angle \: GHI = 14x + 6 = 14 \times 11 + 6 = \boxed{ \tt{160 \degree}}}}[/tex]

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Answer:

6.09 is the answer rounded to nearest hundredths.

Step-by-step explanation:

It gives you n=150, p=0.55, and q=1-p.

If p=0.55 and q=1-p, then by substitution property we have q=1-0.55=0.45.

It ask you to evaluate the expression sqrt(npq).

So npq means find the product of 150 and 0.55 and 0.45. So that is 150(0.55)(0.45)=37.125.

The sqrt(npq) means we need to find the square root of that product. So sqrt(37.125)=6.093 approximately .

Answer:

H0 : ρ = 0

H1 : ρ ≠ 0

Test statistic = 1.197

Pvalue = 0.2335

There is no correlation between the two variables

Step-by-step explanation:

The null and alternative hypothesis :

H0 : No correlation exist,

H1 : Correlation exist

H0 : ρ = 0

H1 : ρ ≠ 0

Test statistic, T = r / √(1 - r²) / (n - 2)

T = 0.067 / √(1 - 0.067²) / (320 - 2)

T = 0.067 / √(0.995511 / 318)

T = 0.067 / 0.0559512

T = 1.197

The Pvalue obtained from the Rscore, at df = 320 - 2 = 318 is 0.2335

α = 5% = 0.05

The Pvalue > α ; we fail to reject the null and conclude that, there is no correlation between the two variables.

Answer:

The answer is "47.5354".

Step-by-step explanation:

In the given graph it is a half-circle and a triangle.

So, the diameter of the circle is 6.2 so the radius is 3.1

[tex]\text{Area of a circle}= \pi r^2\\\\\text{Area of a triangle}= \frac{1}{2} b h\\\\[/tex]

Calculating the total area of the shape:

[tex]= \pi r^2+\frac{1}{2} \times b\times h\\\\ = 3.14 \times 3.1^2+\frac{1}{2} \times 6.2 \times 5.6\\\\ = 3.14 \times 3.1^2+\frac{1}{2} \times 6.2 \times 5.6\\\\=3.14 \times 9.61+\frac{1}{2} \times 34.72\\\\=3.14 \times 9.61+\frac{1}{2} \times 34.72\\\\= 30.1754+17.36\\\\=47.5354\\\\[/tex]

Answer:

B. <B is congruent to the <Z

OPTION B is the correct answer

Answer:

[tex]\frac{3v}{a^{2}} = h[/tex]

Step-by-step explanation:

[tex]v = \frac{1}{3} a^{2} h[/tex]

[tex]3v = a^{2} h[/tex]

[tex]\frac{3v}{a^{2}} = h[/tex]

Answer:

False

Step-by-step explanation:

Points T & W are coplanar. Point Z is on both planes, so it depends on how you see it. HOWEVER, Point U is on another plane (plane Q to be exact), so points T, Z, W, and U are NOT coplanar.

Hope it helps (●'◡'●)

Answer:

a. 7 ÷ 4 yes

b. 4 ÷ 7 no

c. [tex]\frac{7}{4}[/tex] yes

d. [tex]\frac{4}{7}[/tex] no

e. 7 × [tex]\frac{1}{4}[/tex] yes

f. [tex]1\frac{3}{4}[/tex] yes

Step-by-step explanation:

hope this helps ^^

Answer:

d

Step-by-step explanation:

Answer:

[tex]31y^{3} -28y^{2}[/tex]+35y

Step-by-step explanation:

Answer:

By these examples you are able to see that the square of an odd number is always 1 more than a multiple of 4.

Step-by-step explanation:

For examples,

Let's consider squares of 3, 11, 25, 37 and 131.

[tex] {3}^{2} = 9[/tex]

8 is a multiple of 4, and 9 is more than 8.

[tex] {11}^{2} = 121[/tex]

120 is a multiple of 4 and 121 is one more than it.

[tex] {25}^{2} = 625[/tex]

624 is a multiple of 4 and 625 is one more than it.

[tex] {37}^{2} = 1369[/tex]

1368 is a multiple of 4 and 1369 is one more than 1368.

[tex] {131}^{2} = 17161[/tex]

17160 is a multiple of 4.

Answer:

They are supplementary and their sum is 180°

w = 45 + 60 or w = 105

z = 180 - 105 or z = 75

Answer:

4.24 inches

Step-by-step explanation:

1 inch / 50 miles = x / 212 miles      Cross multiply

1 inch * 212 miles = 50 miles * x      Divide by 50 miles

1 inch * 212 miles / 50 miles = x

x = 4.24 inches.

How much is 0.24 of an inch?

0.24 * 50 = 12

So 0.24 inches represents 12 miles.

Answer:

Remember that for an event with a percentage probability X, the probability is given by:

P = X/100%

a) What is the probability that the next customer will request plus gas and fill their tank ?

We know that 35% of the customers use plus gas, and of these using plus, 20% fill their tank.

So the probability that the next customer uses plus gas is:

p = 35%/100% = 0.35

And the probability that the customer fills the tank (given that the customer uses plus gas) is:

q = 20%/100% = 0.2

The joint probability is just the product between the individual probabilities:

Then the probability that the next customer uses plus gas and fills their tank is:

P = 0.35*0.2 = 0.07

b) What is the probability that the next customer fills the tank?

We know that 20% of the ones that use plus gas (with a probability of  0.35) fill their tank, 10% of these that use regular gas (with a probability of 0.4) and 30% of these that use premium (with a probability of 0.25) fill their tank,

Then the probability is computed in a similar way than above, here the probability is:

P = 0.2*0.35 + 0.1*0.4 + 0.3*0.25 = 0.185

The probability that the next customer fills the tank is 0.185

c)  If the next customer fills the tank, what is the probability that the regular gas is requested?

Ok, now we already know that the customer fills the tank.

The probability that a customer uses regular and fills the tank, is

p = 0.1*0.4

The probability that a customer fills the tank is computed above, this is:

P = 0.185

The probability, given that the customer fills the tank, the customer uses regular gas, is equal to the quotient between the probability that the customer fills the tank with regular and the probability that the customer fills the tank, this is:

Probability = p/P = (0.1*0.4)/(0.185) = 0.216

Answer:

-1/2

Step-by-step explanation: