A data set that is normally distributed has a mean of 128 and standard deviation of 6.2. What is the Z-score,
rounded to the nearest hundredth, for a data value of 143

Answer:

a)

0.3632 = 36.32% approximate probability that 15 or fewer turn right.

0.369 = 36.9% exact probability that 15 or fewer turn right.

b)

0.4801 = 48.01% approximate probability that at least two-thirds of those in the sample turn.

0.4868 = 48.68% exact probability that at least two-thirds of those in the sample turn.

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

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

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

Vehicles entering an intersection from the east are equally likely to turn left, turn right, or proceed straight ahead.

This means that [tex]p = \frac{1}{3}[/tex]

50 vehicles

This means that [tex]n = 50[/tex]

Mean and standard deviation:

[tex]\mu = E(X) = np = 50\frac{1}{3} = 16.67[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{50\frac{1}{3}\frac{2}{3}} = 3.33[/tex]

a. 15 or fewer turn right.

Using continuity correction, this is [tex]P(X \leq 15 + 0.5) = P(X \leq 15.5)[/tex], which is the pvalue of Z when X = 15.5. So

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

[tex]Z = \frac{15.5 - 16.67}{3.33}[/tex]

[tex]Z = -0.35[/tex]

[tex]Z = -0.35[/tex] has a pvalue of 0.3632

0.3632= 36.32% approximate probability that 15 or fewer turn right.

Using a binomial probability calculator, to find the exact probability, we get a 0.369 = 36.9% exact probability that 15 or fewer turn right.

b. at least two-thirds of those in the sample turn.

Turn either left or right, so:

[tex]p = \frac{1}{3} + \frac{1}{3} = \frac{2}{3}[/tex]

The standard deviation remains the same, while the mean will be:

[tex]\mu = E(X) = np = 50\frac{2}{3} = 33.33[/tex]

Two thirds of the sample is 33.33, so at least 34 turning, which, using continuity correction, is [tex]P(X \geq 34 - 0.5) = P(X \geq 33.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 33.5.

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

[tex]Z = \frac{33.5 - 33.33}{3.33}[/tex]

[tex]Z = 0.05[/tex]

[tex]Z = 0.05[/tex] has a pvalue of 0.5199

1 - 0.5199 = 0.4801

0.4801 = 48.01% approximate probability that at least two-thirds of those in the sample turn.

Using a binomial probability calculator, we find a 0.4868 = 48.68% exact probability that at least two-thirds of those in the sample turn.

Answer:

The entire clock measures 360 degrees. As the clock is divided into 12 sections. The distance between each number is equivalent to 30 degrees (360/12)

I hope this helps you!

Answer:

14 inches for every side

Step-by-step explanation:

44/4 = 22

circumfrence of half circle is 3.14r = 22

22/3.14 is about 7

the radius is half the side length so multiply 7 by 2 to get 14

mark brainliest please

Answer:

What subject

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

4500 ml kkkkkkkkkkkkkkkkkk

Answer:

6x4=24

Step-by-step explanation:

Answer:

0.0208

Step-by-step explanation:

Using the formula for calculating margin of error is expressed as;

M = z * √p(1-p)/n

z is the z score at 90 % interval

p is the proportion

n is the sample size

p = 0.2

n = 1000

z = 1.645

M = 1.645 * √0.2(1-0.2)/1000

M = 1.645 * √0.2(0.8)/1000

M = 1.645 *  0.01264

M = 0.0208

Hence the margin of error is 0.0208

The polynomial that represents the value of Terryl’s investment after the first year if he invested x dollars in the fund with the lesser growth rate is;

p(x) = x(1 + 6/100)

g(x) = (1500 - x)(1 + 3.8/100)

The compound interest is defined as a form of interest whereby the rate of interest is applied on the amount obtained after every given interval of time.

We are given that;

The total amount invested in the two mutual funds = $1500.

The growth rate of the first mutual fund = 6%.

The growth rate of the second mutual fund = 3.8%.

If the amount invested in the first mutual fund is x, then the amount invested in second mutual fund is 1500 - x.

The growth for both mutual funds can then be represented by;

First mutual fund; p(x) = x(1 + 6/100)

The second mutual fund; g(x) = (1500 - x)(1 + 3.8/100)

Thus, the polynomial expression for both the mutual funds are;

p(x) = x(1 + 6/100) and g(x) = (1500 - x)(1 + 3.8/100) respectively.

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Answer:

Step-by-step explanation:

6²+8²=36+64=100=10²

so it is a right angled triangular prism.

surface area=2×(1/2 ×8×6)+(6+8+10)×7

=48+980

=1028 sq. m.

Answer:

225.32

Step-by-step explanation:

Hope this helped :)

Answer:

bc

Step-by-step explanation:

Answer bc

Step-by-step explanation:

took test

Answer:

530

Step-by-step explanation:

870-340 = 530

___________

Answer:

[tex]x > -3.5[/tex]

Step-by-step explanation:

Given

[tex]-6x < 21[/tex]

Required

Plot a number line

First, solve for x

[tex]-6x < 21[/tex]

Divide by -6

[tex]\frac{-6x}{-6} > \frac{21}{-6}[/tex]

[tex]x > -3.5[/tex]

See attachment for number line

Answer:

850

Step-by-step explanation:

Answer:

850

Step-by-step explanation:

34*100=3400

3400/4=850

Would be amazing if you marked this as brainliest

Answer: B.

Step-by-step explanation:

9514 1404 393

Answer:

  4%

Step-by-step explanation:

The amount of simple interest is given by ...

  I = Prt . . . . . amount P invested at annual rate r for t years

This can be solved for r:

  r = I/(Pt)

Using the given values, we find the rate to be ...

  r = 16/(200·2) = 16/400 = 4/100 = 4%

The annual interest rate is 4%.

All of the clients of the insurance company are the population, and the parameter is the annual average cost of health care for all of the clients of the insurance company.

A variable in mathematics is a word or an alphabet that stands in for an unknowable quantity, value, or number. In the context of algebra or algebraic expression, the variables are employed specifically. Consider the linear equation x+9=4, which has 9 and 4 as constants and uses x as a variable.  There are many variables, including height, age, wealth, province of birth, academic standing, and kind of dwelling. The independent variable is often plotted on the x-axis whereas the dependent variable is typically plotted on the y-axis. The independent variable's value also determines

given

Information: The 400 clients' annual health care costs that the insurance provider included in the analysis.

-Variable: The expense of health care per year

400 clients were used as a sample in this study by the insurance business.

The insurance provider included 400 consumers in this survey, providing statistics on the average annual cost of health care for each of them.

-Parameter: The annual average cost of health care for all customers of the insurance provider.

All of the clients of the insurance company are the population, and the parameter is the annual average cost of health care for all of the clients of the insurance company.

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Answer:

3 examples of mechanical digestion:

Mastication

Swallowing

Peristalsis

Answer: ok so 3 times 3 twice then divide them by 2 and then 12 times 3 twice and then 3 times 6 im pretty sure and then you add them together

Step-by-step explanation:

Answer:

171 degrees

Step-by-step explanation:

x + 9 = 180

x = 171

Answer:

8.04% to 15.96%

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

Suppose that you take a random sample of 259 people leaving a grocery store over the course of a day and find that 12% of these people were overcharged.

This means that [tex]n = 259, \pi = 0.12[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.12 - 1.96\sqrt{\frac{0.12*0.88}{259}} = 0.0804[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.12 + 1.96\sqrt{\frac{0.12*0.88}{259}} = 0.1596[/tex]

So 8.04% to 15.96%

sinx-✓(1-3sin2x)=0

-✓(1-3sin2x)=-sinx

apply squared both sides

(-✓(1-3sin2x)^2=(-sinx)^2

1-3sin2x=sin2x

collect like terms

-3sin2x-sin2x+1=0

-4sin2x+1=0

-4sin2x=-1

devide both sides by -4

sin2x=-1/-4

sin2x=0.25

sinx*sinx =0.25

[sinx]^2 = 0.25

apply square root both sides

180-x= Theta(X)

180-30=X

X=150°

therefore, all angles for sinx -✓(1-3sin2x)=0 are (X= 30° and 150°)

Answer:

D

Step-by-step explanation:

If the necklace must cost less than $12.75, then it would be shown either $12.75 > p (being greater than p) or p < $12.75 ( meaning that P is worth less than $12.75. And with that, the cost must have a maximum of $12.75 making D the answer.

Answer:False

Step-by-step explanation:

Answer:

x = 20

Step-by-step explanation:

The small square at the vertex indicates a 90º angle

Therefor

x + (3x + 10) = 90

Combine like terms

4x + 10 = 90

Subtract 10 from both sides

4x = 80

Divide both sides by 4

x = 20

Answer:

Test statistic = 3.21;

Pvalue = 0.0019;

Reject H0 and conclude that the mean conversion rate is greater than 30.

Step-by-step explanation:

Hypothesis :

NULL ; H0 : μ = 30

ALTERNATIVE ; H0 : μ > 30

Sample, x : 52.3 41.1 28.8 67.8 78.6 72.3 9 19.0 30.3 41.0 63.0 80.8 26.8 37.3 38.1 33.6 14.3 30.1 33.4 36.2 34.6 40.0 81.2 59.4

Sample Mean, xbar = 43.71 (using calculator)

Sample standard deviation, s = 20.95 ( calculator)

Sample size, n = 24

Take, α = 0.05

Test statistic :

(xbar - μ) ÷ (s/√n)

(43.71 - 30) ÷ (20.95/√24)

13.71 / 4.2764008

Test statistic = 3.21

Degree of freedom, df = n - 1 = 24 - 1 = 23

The Pvalue, using a Pvalue calculator : (3.21, 23)

Pvalue = 0.001942

Pvalue = 0.0019 ( 4 decimal places).

Decison :

Reject H0 ; if Pvalue ≤ α

Since Pvalue is very low and lesser than α ` We reject H0 and conclude that the mean conversion rate is greater than 30.

Using the provided quadratic expression and factorizing it, The answer is  x = ± √6.4 or x = ± 2.51 and  x = 1 or x = -2.5 .

An equation is a statement of equality between two expressions. It typically includes numbers and mathematical operations such as addition, subtraction, multiplication, and division. For example, the equation 2x + 3 = 7 is a statement that the value of the expression 2x + 3 is equal to the value of 7. Equations can also include variables, which represent unknown values that can be solved for.

Roots of an equation are the values of the variable that make the equation true. For example, the roots of the equation x^2 + 2x - 3 = 0 are -1 and 3, because (-1)^2 + 2(-1) - 3 = 0 and 3^2 + 2(3) - 3 = 0. In general, finding the roots of an equation can be a difficult task and may require the use of mathematical techniques such as factoring, graphing, or numerical methods. Roots are also known as solutions or zeroes of an equation. They can be found by setting the equation equal to zero and solving for the variable.

(4+5x²-36) = 0 or (2x²+9x-5) = 0

Solving the first factor:

4+5x²-36 = 0

5x²-32 = 0

5x² = 32

x² = 6.4

x = ± √6.4

x = ± 2.51 or -2.51

Solving the second factor:

2x²+9x-5 = 0

x²+4.5x-2.5 = 0

(x-1)(x+2.5) = 0

x = 1 or x = -2.5

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First, we assume that this conclusion is false. In other words, we assume that the contrary statement "none of the two angles has measure [tex]90^{\circ}[/tex] or greater" is true.

The assumption is equivalent to the following two statements:

(1) [tex]m\angle A\text{ } \boxed{ < 90^{\circ}}[/tex]

(2) [tex]m\angle B\text{ } \boxed{ < 90^{\circ}}[/tex]

Using (1) and (2) and the addition properties of inequalities, we conclude that [tex]m\angle A+m\angle B \text{ } \boxed{ < } \text{ } 180^{\circ}[/tex].

On the other hand, two adjacent angles form a linear pair. Thus, the last statement contradicts the Linear Pair Property, which states that for a linear pair of angles [tex]\angle A[/tex] and [tex]\angle B[/tex], [tex]m\angle A+m\angle B \text{ } \boxed{=} \text{ } 180^{\circ}[/tex].

Therefore, the assumption made is false, and the statement "at least one of the angles [tex]\angle A[/tex] and [tex]\angle B[/tex] has measure [tex]90^{\circ}[/tex] or greater" is true.