Television viewing reached a new high when the global information and measurement company reported a mean daily viewing time of hours per household. Use a normal probability distribution with a standard deviation of hours to answer the following questions about daily television viewing per household.
a. what is the probability that a household views television between 6 and 8 hours a day (to 4 decimals)?
b. How many hours of television viewing must a household have in order to be in the top 5% of all television viewing households (to 2 decimals)?
c. What is the probability that a household views television more than 5 hours a day (to 4 decimals)?

Answer:

no solution

Step-by-step explanation:

4( − 11) = 15 − 4

-44 = 11

Since this iS FALSE, it means that the equation given has no solution

Answer:

P = 4/13

Step-by-step explanation:

In a deck of 52 cards, there are 3 aces(spade, heart, diamond), 1 club ace, and 12 remaining club cards

=> The probability of randomly drawing 1 card that is an ace card or a club card:

P = number of elements/total number of elements

P = (3 + 1 + 12)/52

P = 16/52

P = 4/13

=> Option A is correct

Answer:

[tex]x^{4} -11x^{2} +28[/tex]

Step-by-step explanation:

[tex](x^{2} -7)(x^{2} -4)[/tex]

[tex]x^{4} -4x^{2} -7x^{2} +28[/tex]

[tex]x^{4} -11x^{2} +28[/tex]

Answer:

Answers are below in bold.

Step-by-step explanation:

The first answer is correct. 1 m² = 10,000cm²

A=2(wl+hl+hw)        To find the surface area of the package, use this equation

A=2(18*50+20*50+20*18)      Multiply in the parentheses

A=2(900+1000+360)             Add in the parentheses

A=2(2260)                              Multiply

A=4520

The package has a surface area of 4520 cm²

The area of the package is less than the area of the wrapping paper.

So, Dayson can completely cover the package with the wrapping paper.

Answer:

The miner should take door number 1

Answer:

11.49 dogs/ square mile

Step-by-step explanation:

Population density of any place is number of living being living in that area per unit area.

Population density = number of living being/ area of the place

given

number of dogs= 43,600,000

area = 3,794,083 square miles

population density of domesticated dogs = 43,600,000 /3,794,083

                                                              = 11.4915 dogs/ square mile

population density of domesticated dogs, rounded to the nearest 10th

                                                              is  11.49 dogs/ square mile.

Answer:

I have two types of packages that i sell. one has 3 apples and 10 pears, another one has 5 apples and 20 pears. what are the minumum quantitys of each do i have to buy so i can make either all package #1 or only make package#2 with oout any left over pears and apples?

Step-by-step explanation:

i don't know how to explain it but i;ll try. you take the lcm i beleive of the two. i think i may have done it wrong

Answer:

spinner green or blue

Step-by-step explanation:

Flipping a coin is 1/2 probability

Rolling a die and getting a number less than 4 is 1/2 probability

spinner green or blue is (4/6) = 2/3

Marbles is 1/2

Answer:

c. 0.80

Step-by-step explanation:

Probability from relative frequency:

The probability is the number of desired outcomes divided by the number of total outcomes.

What is the probability that the next bus sold will be yellow or green?

250+150+100 = 500 buses sold

Of those, 250+150 = 400 are yellow or green.

400/500 = 0.8

So the correct answer is:

c. 0.80

Answer:

y = 4.5x

Step-by-step explanation:

y=ax is form of proportional relationship

checking the first pair of numbers:

checking other lines

So the equation is:

Answer:

112 ounces

Step-by-step explanation:

Clay weighs 9 times as much as his baby sister .

Clay weighs 63 pounds.

His baby sister weigh 63/9.

His baby sister weighs 7 pounds.

But to be converted to ounce.

1 pound = 16 ounces

7 pounds = 7*16 ounces

7 pounds = 112 ounces

Answer:

[tex]150-2.797\frac{35}{\sqrt{25}}=130.421[/tex]    

[tex]150+2.797\frac{35}{\sqrt{25}}=169.579[/tex]    

Step-by-step explanation:

Information given

[tex]\bar X=150[/tex] represent the sample mean for the sample  

[tex]\mu[/tex] population mean

s=35 represent the sample standard deviation

n=25 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:

[tex]df=n-1=25-1=24[/tex]

Since the Confidence is 0.99 or 99%, the value of [tex]\alpha=0.01[/tex] and [tex]\alpha/2 =0.005[/tex] and the critical value for this case [tex]t_{\alpha/2}=2.797[/tex]

Now we have everything in order to replace into formula (1):

[tex]150-2.797\frac{35}{\sqrt{25}}=130.421[/tex]    

[tex]150+2.797\frac{35}{\sqrt{25}}=169.579[/tex]    

Answer:

17000

Step-by-step explanation:

we can use the equation I=PRT

I=10,000(10)(0.07)

I=100,000(0.07)

i=7000

7000+ the initial 10,000=17000

Answer:

work is shown and pictured

Answer:

  9/8

Step-by-step explanation:

time A / time B = (3/2)/(4/3) = (3/2)(3/4) = (3·3)/(4·2)

time A / time B = 9/8

Answer:

Step-by-step explanation:

Since we know that for a distribution be a probability density function sum of all the probability events should be equal to 1 and all individual events should have probability between 0 and 1

a. x P(X=x)

0 -----3/8

1 -----1/4

2 -----3/8

P(X=0)+P(X=1)+P(X=2) = 3/8 + 1/4 + 3/8

P(X=0)+P(X=1)+P(X=2) = 6/8 + 2/8 = 1

This is a probability density function

b. x P(X=x)

0 ----0.2

1 ----0.1

2 ----0.35

3 ----0.17

P(X=0)+P(X=1)+P(X=2)+P(X=3) = 0.2 + 0.1 + 0.35 + 0.17

P(X=0)+P(X=1)+P(X=2)+P(X=3) = 0.65 + 0.17 = 0.82 ≠ 1

Therefore this is NOT a probability density function

c. x P(X=x)

0---- 9/10

1 ---- −3/10

2 ---- 3/10

3 ---- 1/10

Since P(X=1) is not between 0 and 1

Therefore this is NOT a probability density function

d. x P(X=x)

0 ----0.06

1 ----0.01

2 ----0.07

3 ----0.86

P(X=0)+P(X=1)+P(X=2)+P(X=3) = 0.06 + 0.01 + 0.07 + 0.86

P(X=0)+P(X=1)+P(X=2)+P(X=3) = 0.14 + 0.86 = 1

Therefore this is a probability density function

e. x P(X=x)

0 ----1/2

1 ----1/8

2 ----1/4

3 ----1/8

P(X=0)+P(X=1)+P(X=2)+P(X=3) = 1/2 + 1/8 + 1/4 + 1/8

P(X=0)+P(X=1)+P(X=2)+P(X=3) = 1/2 + 1/2 = 1

Therefore this is a probability density function

f. x P(X=x)

0 ----1/10

1 ----1/10

2 ----3/10

3 ----1/5

P(X=0)+P(X=1)+P(X=2)+P(X=3) = 1/10 + 1/10 + 3/10 + 1/5

P(X=0)+P(X=1)+P(X=2)+P(X=3) = 2/10 + 5/10 = 7/10 ≠ 1

Answer:

27.41%

Step-by-step explanation:

Data provided in the question

The staffed of Alpha company = 79%

The staffed of Beta company = 62%

Based on the above information, the relative change of staffing from Alpha to beta company is

As we know that

[tex]\bold {\ Relative \ change = \frac{\alpha- \beta }{\beta }}[/tex]

[tex]= \frac{(79 -62)}{62} \% \\\\= \frac{17}{62} \times 100\\\\=0.2741 \times 100\\\\=27.41\ \%[/tex]

By applying the above formula we can get the relative change and the same is to be applied so that the correct percentage could come

Answer:

the graph of y=f(x)will shift up 9 units

Answer:

Dimensions 30 in x 30 in x 15 in

Surface Area = 2,700 in²

Step-by-step explanation:

Let 'r' be the length of the side of the square base, and 'h' be the height of the bin. The volume is given by:

[tex]V=13,500=h*r^2\\h=\frac{13,500}{r^2}[/tex]

The total surface area is given by:

[tex]A=4*hr+r^2[/tex]

Rewriting the surface area function as a function of 'r':

[tex]A=4*\frac{13,500}{r^2} *r+r^2\\A=\frac{54,000}{r}+r^2[/tex]

The value of 'r' for which the derivate of the surface area function is zero, is the length for which the area is minimized:

[tex]A=54,000*r^{-1}+r^2\\\frac{dA}{dr}=0= -54,000*r^{-2}+2r\\\frac{54,000}{r^2}=2r\\ r=\sqrt[3]{27,000}\\r=30\ in[/tex]

The value of 'h' is:

[tex]h=\frac{13,500}{30^2}\\ h=15\ in[/tex]

The dimensions that will ensure the minimum surface area are 30 in x 30 in x 15 in.

The surface area is:

[tex]A=4*15*30+30^2\\A=2,700\ in^2[/tex]

Answer:

[tex]P(52<X<70)=P(\frac{52-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{70-\mu}{\sigma})=P(\frac{52-60}{9.4}<Z<\frac{70-60}{9.4})=P(-0.851<z<1.064)[/tex]

And we can find this probability with this difference:

[tex]P(-0.851<z<1.064)=P(z<1.064)-P(z<-0.851)[/tex]

And if we use the normal standard distribution or excel we got:

[tex]P(-0.851<z<1.064)=P(z<1.064)-P(z<-0.851)=0.856-0.197=0.659[/tex]

Step-by-step explanation:

Let X the random variable that represent the time required to construct and test a particular component of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(60,9.4)[/tex]  

Where [tex]\mu=60[/tex] and [tex]\sigma=9.4[/tex]

We want to find this probability:

[tex]P(52<X<70)[/tex]

And the best way to solve this problem is using the normal standard distribution and the z score given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Using this formula we got:

[tex]P(52<X<70)=P(\frac{52-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{70-\mu}{\sigma})=P(\frac{52-60}{9.4}<Z<\frac{70-60}{9.4})=P(-0.851<z<1.064)[/tex]

And we can find this probability with this difference:

[tex]P(-0.851<z<1.064)=P(z<1.064)-P(z<-0.851)[/tex]

And if we use the normal standard distribution or excel we got:

[tex]P(-0.851<z<1.064)=P(z<1.064)-P(z<-0.851)=0.856-0.197=0.659[/tex]

Answer:

w = 9, l = 12

Step-by-step explanation:

If w is the width and l is the length, then:

l = 2w − 6

The area of the rectangle is width times length.

A = wl

Substituting and solving:

108 = w (2w − 6)

108 = 2w² − 6w

54 = w² − 3w

0 = w² − 3w − 54

0 = (w + 6) (w − 9)

w = -6 or 9

The width is 9, so the length is 12.

Answer:

99.27%

Step-by-step explanation:

We have to:

sample size (n) = 100

p = 0.8

1 egg = 3 * 0.01 = 0.03

eggs = 100 - 30 broken eggs = 70

Let's find the probability of winning more than $ 1.30 today:

p (x> 1.30) = p (z, (x -m) / sd)

average earnings:

per day would be:

m1 = 100 / 1.5 * 0.8 * 0.03

m1 = 1.6

sd1 = (m1 * (1 - p)) ^ (1/2) = (1.6 * (1 - 0.8)) ^ (1/2)

sd1 = 0.566

earnings for broken eggs:

m2 = 70 * 0.8 * 0.03

m2 = 1.68

sd2 = (m2 * (1 - p)) ^ (1/2) = (1.68 * (1 - 0.8)) ^ (1/2)

sd2 = 0.58

Now the total profit would be:

m = m1 + m2 = 1.6 + 1.68

m = 3.28

sd = sd1 ^ 2 + sd2 ^ 2 = 0.566 ^ 2 + 0.58 ^ 2

sd = 0.81

now yes, replacing:

p (x> 1.30) = p (z> (1.3 - 3.28) /0.81)

p (x> 1.30) = p (z> -2.44)

for this z = 0.0073

Therefore the probability would be:

1 - 0.0073 = 0.9927

That is, we would have a 99.27% probability of achieving the goal.

Answer:

AP = 10

Step-by-step explanation:

According to secant-secant theorem

(PB)(AP)=(PD)(PC)

6(AP) = (5)(12)

AP = 60/6

AP = 10

Answer:

10

Step-by-step explanation:

Applying the secant theorem, we get:

(PB) * (AP) = (PD) * (PC)

6 * (AP) = (5) * (12)

AP = 60/6

= 10

Hope this helps!

Answer:

a) 0.6628 = 66.28% probability that at least 85 visitors had a recorded entry through the Beaver Meadows park entrance

b) 0.5141 = 51.41% probability that at least 80 but less than 90 visitors had a recorded entry through the Beaver Meadows park entrance

c) 0.5596 = 55.96% probability that fewer than 12 visitors had a recorded entry through the Grand Lake park entrance.

d) 0.9978 = 99.78% probability that more than 55 visitors have no recorded point of entry

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 samples 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].

In this problem, we have that:

[tex]n = 175[/tex]

(a) What is the probability that at least 85 visitors had a recorded entry through the Beaver Meadows park entrance?

46.7% of visitors to Rocky Mountain National Park in 2018 entered through the Beaver Meadows. This means that [tex]p = 0.467[/tex]. So

[tex]\mu = E(X) = np = 175*0.467 = 81.725[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{175*0.467*0.533} = 6.6[/tex]

This probability, using continuity correction, is [tex]P(X \geq 85 - 0.5) = P(X \geq 84.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 84.5. So

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

[tex]Z = \frac{84.5 - 81.725}{6.6}[/tex]

[tex]Z = 0.42[/tex]

[tex]Z = 0.42[/tex] has a pvalue of 0.6628.

66.28% probability that at least 85 visitors had a recorded entry through the Beaver Meadows park entrance.

(b) What is the probability that at least 80 but less than 90 visitors had a recorded entry through the Beaver Meadows park entrance?

Using continuity correction, this is [tex]P(80 - 0.5 \leq X <  90 - 0.5) = P(79.5 \leq X \leq 89.5)[/tex], which is the pvalue of Z when X = 89.5 subtracted by the pvalue of Z when X = 79.5. So

X = 89.5

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

[tex]Z = \frac{89.5 - 81.725}{6.6}[/tex]

[tex]Z = 1.18[/tex]

[tex]Z = 1.18[/tex] has a pvalue of 0.8810.

X = 79.5

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

[tex]Z = \frac{79.5 - 81.725}{6.6}[/tex]

[tex]Z = -0.34[/tex]

[tex]Z = -0.34[/tex] has a pvalue of 0.3669.

0.8810 - 0.3669 = 0.5141

51.41% probability that at least 80 but less than 90 visitors had a recorded entry through the Beaver Meadows park entrance

(c) What is the probability that fewer than 12 visitors had a recorded entry through the Grand Lake park entrance?

6.3% of visitors entered through the Grand Lake park entrance, which means that [tex]p = 0.063[/tex]

[tex]\mu = E(X) = np = 175*0.063 = 11.025[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{175*0.063*0.937} = 3.2141[/tex]

This probability, using continuity correction, is [tex]P(X < 12 - 0.5) = P(X < 11.5)[/tex], which is the pvalue of Z when X = 11.5. So

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

[tex]Z = \frac{11.5 - 11.025}{3.2141}[/tex]

[tex]Z = 0.15[/tex]

[tex]Z = 0.15[/tex] has a pvalue of 0.5596.

55.96% probability that fewer than 12 visitors had a recorded entry through the Grand Lake park entrance.

(d) What is the probability that more than 55 visitors have no recorded point of entry?

22.7% of visitors had no recorded point of entry to the park. This means that [tex]p = 0.227[/tex]

[tex]\mu = E(X) = np = 175*0.227 = 39.725[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{175*0.227*0.773} = 5.54[/tex]

Using continuity correction, this probability is [tex]P(X \leq 55 + 0.5) = P(X \leq 55.5)[/tex], which is the pvalue of Z when X = 55.5. So

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

[tex]Z = \frac{55.5 - 39.725}{5.54}[/tex]

[tex]Z = 2.85[/tex]

[tex]Z = 2.85[/tex] has a pvalue of 0.9978

0.9978 = 99.78% probability that more than 55 visitors have no recorded point of entry

Answer:

-2> 7+35

-2>42

0<21

the answer is 0 is less than 21

Answer:

These two statements are equivalent because statement A is the contrapositive of statement B.

Step-by-step explanation:

In logic, when we have an "if" statement we can have its contrapositive or its converse.

Given a "if p, then q" (p is the hypothesis and q is the conclusion), the converse is "if q, then p", in other words, we interchange the hypothesis and the conclusion.

Now, given a "if p, then q", the contrapositive is "if not q, then not p". In other words, we take the negation of both the hypothesis and the conclusion and then we interchange them.

Now, let's take a look at our statements:

If a and b are two real numbers, and if ab = 0, then either a = 0 or b = 0.

In this case:

p = a and b are two real numbers and ab=0

q = either a = 0 or b = 0

Now, let's take the negative of p and q:

The negative of p would be: a and b are two real numbers and their product is not zero.

The negative of q would be: neither of the two real numbers is zero

Now, given than the contrapositive is "if not q, then not p" we would have:

If neither of two real numbers is zero, then their product is not zero.

We can see that this last sentence is the contrapositive of the first one and thus:

These two statements are equivalent because statement A is the contrapositive of statement B.

Answer:

Yes, her reasoning is correct

Step-by-step explanation:

Given the ratio:  109.2 : 6

Written in fractional form, we have:

[tex]109.2: 6=\dfrac{109.2}{6}[/tex]

Now:

[tex]\dfrac{109.2}{6}=\dfrac{109.2}{6}X1, $ Let 1=\dfrac{10}{10}, \\\\=\dfrac{109.2}{6}X\dfrac{10}{10}\\\\=\dfrac{1092}{60}[/tex]

Therefore, the student's reasoning is correct. In fact, as a check:

[tex]\dfrac{109.2}{6}=18.2\\\\\dfrac{1092}{60}=18.2[/tex]

We would obtain the same result in both cases.

Answer:

yes

Step-by-step explanation:

Answer:

1) -4/5,3 Decimal form x= -0.8,3

2) ?

3)sq (x+2)(x+3)+sq x^2 +5x-4=0

Step-by-step explanation:

Hope this helps