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Answer:

a. 0.6826 = 68.26% probability that a randomly selected x-value from the distribution is between 29 and 37.

b. 0.4987 = 49.87% probability that a randomly selected x-value from the distribution is between 33 and 45.

c. 0.8413 = 84.13% probability that a randomly selected x-value from the distribution is at least 29.

d. 0.8413 = 84.13% probability that a randomly selected x-value from the distribution is at most 37.

Step-by-step explanation:

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 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.

A normal distribution has a mean of 33 and a standard deviation of 4.

This means that [tex]\mu = 33, \sigma = 4[/tex]

a. between 29 and 37

This is the pvalue of Z when X = 37 subtracted by the pvalue of Z when X = 29. So

X = 37

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

[tex]Z = \frac{37 - 33}{4}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a pvalue of 0.8413

X = 29

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

[tex]Z = \frac{29 - 33}{4}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a pvalue of 0.1587

0.8413 - 0.1587 = 0.6826

0.6826 = 68.26% probability that a randomly selected x-value from the distribution is between 29 and 37.

b. between 33 and 45

pvalue of Z when X = 45 subtracted by the pvalue of Z when X = 33. So

X = 45

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

[tex]Z = \frac{45 - 33}{4}[/tex]

[tex]Z = 3[/tex]

[tex]Z = 3[/tex] has a pvalue of 0.9987

X = 33

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

[tex]Z = \frac{33 - 33}{4}[/tex]

[tex]Z = 0[/tex]

[tex]Z = 0[/tex] has a pvalue of 0.5

0.9987 - 0.5 = 0.4987

0.4987 = 49.87% probability that a randomly selected x-value from the distribution is between 33 and 45.

c. at least 29

This is 1 subtracted by the pvalue of Z when X = 29. So

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

[tex]Z = \frac{29 - 33}{4}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a pvalue of 0.1587

1 - 0.1587 = 0.8413

0.8413 = 84.13% probability that a randomly selected x-value from the distribution is at least 29.

d. at most 37

This is the pvalue of Z when X = 37. So

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

[tex]Z = \frac{37 - 33}{4}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a pvalue of 0.8413

0.8413 = 84.13% probability that a randomly selected x-value from the distribution is at most 37.

Following are the solution to the given points:

Given:

[tex]\to Mean \ (\mu)= 33\\\\ \to \text{standard deviation}\ (\sigma) =4 \\\\[/tex]

To find:

find points=?

Solution:

For point a:

[tex]\to P (29 <x<37) = P(\frac{29-33}{4} \leq \frac{X-\mu}{\sigma} \leq \frac{37-33}{4} )[/tex]

                              [tex]= P(\frac{-4}{4} \leq \frac{X-\mu}{\sigma} \leq \frac{4}{4} )\\\\= P(-1 \leq z \leq 1 )\\\\= P(-1 < z <1 )\\\\= P(Z <+1) - P(Z <-1) \\\\=0.84134 - 0.15866\\\\= 0.68268 \\\\=68.268\%[/tex]

For point b:

[tex]\to P (33 <x<45) = P(\frac{33-33}{4} \leq \frac{X-\mu}{\sigma} \leq \frac{45-33}{4} )[/tex]

                 [tex]= P(\frac{0}{4} \leq \frac{X-\mu}{\sigma} \leq \frac{12}{4} )\\\\= P(\frac{0}{4} \leq \frac{X-\mu}{\sigma} \leq 3 )\\\\= P(-2< z< 0)\\\\= P(Z <-2) - P(Z <0) \\\\=0.9987-0.5 \\\\= 0.4987\\\\= 49.87\%[/tex]  

For point c:

When X = 29, subtract by 1 from the p-value of Z.

Using formula:

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

        [tex]=\frac{29-33}{4} \\\\ =\frac{-4}{4} \\\\= -1 \\\\=1 - 0.1587 \\\\= 0.8413 \\\\= 84.13\%[/tex]

For point d:

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

        [tex]= \frac{37-33}{4}\\\\ =1\\\\ =\text{1 has a p-value of}\ 0.8413\\\\=0.8413 \\\\= 84.13\%[/tex]

So, the answer is " 68.268%,49.87%, and 84.13%"

Learn more about the normal distribution:

brainly.com/question/12421652

Answer:

15 years (180 months)

Step-by-step explanation:

turn it into months first

147

216

163

206

180

168

add them together, then divide by how many there are

1,080/6=180 months

180/12 =15

Answer:

rajjsjdjdjxkkdkdkdkkdjxjjdjxjckfkjdjfuidid

Answer:

Step-by-step explanation:

Put the equation into vertex form.

y = 2x² + 10x + 8

= 2(x² + 5x) + 8

= 2(x² + 5x + 2.5²) - 2·2.5² + 8

= 2(x+2.5)² - 4.5

vertex (-2.5, -4.5)

Answer:

6

Step-by-step explanation:

16=n +10

subtract 10 from both sides and your left with 6=n

Answer:

1.75

Step-by-step explanation:

nsjdjdjdjdjndnsjdjdjjddbjdjsjsj its 1.75

Answer:

7/4

Step-by-step explanation:

3/4 * 2 1/3 = 7/4

Hope this helps =]

Answer:

See Explanation

Step-by-step explanation:

For an object at temperature T and supposing that the ambient temperature is Ta then we can write the differential equation that typifies the Newton law of cooling as follows;

dT/dt=-k(T-Tₐ)

So

dT/dt = 2 degrees Celsius per minute

T = 70 degrees Celsius

Ta = 25 degrees Celsius

2 = -k(70 - 25)

-k = 2/(70 - 25)

k = - 0.044

Hence we can write;

dT/dt=-(- 0.044)(95-25)

dT/dt= 3 degrees Celsius per minute

Answer:

7

Step-by-step explanation:

The range is the distance between the largest and smallest number. So 9-2=7

Hope this helped!

Answer: 9-2=7

Step-by-step explanation:Range is the highest value minus the lowest value in the data set.

Answer:

1 3/40, or  1.075!

Step-by-step explanation:

Please tell me if i made a mistake or misunderstood.

Answer:b

Step-by-step explanation: use pemdas

Answer:

The answer is b. 0.029

Step-by-step explanation:

Margin error for a sample size of 1200 is 2.9%.

The Margin error formula can be represented as:

[tex]z \times \: \sqrt{ \frac{p0(1 - po)}{n} } [/tex]

Where

z = critical value

n = sample size

[tex]p0 = sample \: proportion[/tex]

Answer:

C

Step-by-step explanation:

Use the slope formula:

m = (y2 - y1) / (x2 - x1)

m = (-3 - 2) / (5 - 3)

m = -5/2

Answer:

Elder brother: 25

Younger brother: 5

Step-by-step explanation:

38 - (4+4)= 30

Now trial all square numbers

e.g 2 + 4 = 6 (does not work)

5 + (5x5)= 30

Answer:

mode is 10 as it is repeated more

Answer:

In this case, the net effect is that you moved the decimal point three places to the right, which is the same as multiplying 7 by 1,000.Step-by-step explanation:

the correct answer is b

Answer is in the file below

tinyurl.com/wpazsebu

Area of square pyramid:

⅓×[base area]×height

according to the question

⅓×[8×8]×12

simplify parentheses:

⅓×64×12

Simplify fraction

64×4

Simplify multiplication

256

256      did the test on k12 Answer:

c

Step-by-step explanation:

Answer:

Coefficient is your answer

Answer:

3 is a coefficient

Step-by-step explanation:

a constant is a number without a variable and that is unchanging

3 has the variable w attached to it and will change with the value of w

hope this helps <3

Answer:

A: 1800h-25,000

B: Yes, he would have time.

Step-by-step explanation:

A:

Lets turn 30 gallons/minute into hours so we can make it easier.

18000h-25000

Then plug in h which is hours. To get your answer

B:

From May 7 at 8:00 a.m. to May 8 at 12 p.m. would be 28 hours.

So we plug in 28 for h and get our answer of 25400 gallons/hour

Answer: The answer is 7mn+3m/2+5n/4

7mn + 3m/2 + 5n/4 is the algebraic expression which is a polynomial

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

A polynomial is an expression with variables and coefficients separated by addition and subtraction.

The following are used when determining if an expression is a polynomial:

i) Variables of a polynomial must not have negative exponent.

ii) Variables of a polynomial must not have fractional exponent.

iii) Dividing by an exponent is not allowed

iv) Exponent radicals are not allowed.

7mn + 3m/2 + 5n/4 is a polynomial because it has variables and seperated by operators addition and subtraction.

Hence, 7mn + 3m/2 + 5n/4 is the algebraic expression which is a polynomial

To learn more on Polynomials click:

https://brainly.com/question/11536910

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Answer:

Hey mate.....

Step-by-step explanation:

This is ur answer....

Hope it helps you,

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Follow me! :)

Answer:

I think the answer is A as well

Step-by-step explanation:

Answer:

a a a a a a a a  a a a a  a

Step-by-step explanation:

Answer:

4.05 dollars

Step-by-step explanation:

4 dollars and 5 cents. 15 percent of 27 is 4.05

Answer:

When t = 3, y = 12.  y = 4t, for t>0

Step-by-step explanation:

8 = 4 x 2; y = 4 x 3 = 12.

Answer:

51°

Step-by-step explanation:

35°+(2x+16)°+(4x+3)°=360°

54°+6x=360°

6x=360°-54°

6x=306°

x=306°/6

x=51°

Answer:

The value of p is 1

Step-by-step explanation:

we know that  

The standard form of the equation of a horizontal parabola is

(y - k)² = 4p(I - h)

where

(h,k) is the vertex

p[tex]\neq[/tex] 0

if p > 0, the parabola opens to the right, and if p < 0, the parabola opens to the left.

In this problem we have

I = [tex]\frac{1}{4}[/tex]y²

Convert to standard form

y² 4I

The vertex is the point (0,0)

4p = 4

P = 1 -----> p > 0, the parabola opens to the right  

Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

if the realtor received a commission of 17,500 dollars which represent only 7% of the price of the house,

the sale price was

(17,500*100)/0.07=250,000

Answer:

a. percentage of children with myopia = 24.87%

b. 3.23% of children living in Australia have myopia

29.14% 0f children living in Singapore have myopia

Step-by-step explanation:

a.

the table is an attachment

percentage of children with myopia in this study

number of children with myopia in Australia = 4

number of children with myopia in Singapore = 183

total children with myopia = 4 + 183 = 187

total number of Australian children = 124

total number of Singapore children = 628

total number of children = 124 + 628 = 752

percentage with myopia = 187/752 * 100 = 24.87%

2.

percentage of Australian children with myopia

total children from Australia = 124

those with myopia = 4

percentage = 4/124 * 100 = 3.23% of children living in Australia have myopia

percentage of Singapore children with myopia

total number of children = 628

those with myopia = 183

percentage = 183/628 * 100 = 29.14% 0f children living in Singapore have myopia

Answer:

-7.

Step-by-step explanation:

(x²+t²x+t³+8)`=(x²)`+(t²x)`+(t³)`+(8)`=2x*x'+2t*x+t²*x'+3t²;

[tex]x'=\frac{2tx+3t^2}{t^2+2x};[/tex]

[tex]x'(-2;-4)=\frac{2*2*4+3*4}{4-8}=-7.[/tex]