Answer:
12 boxes.
Step-by-step explanation:
We need to find the greatest common factor of 251 and 180:
First find the prime factors :
252 = 2*2*3*3*7
180 = 2*2*3*3*5
So the GCF = 2*2*3*3 = 36.
So id each box is identical, there could be 7 boxes of dark chocolates and 5 boxes of milk chocolates each containing 36 chocolates.
Total number of boxes = 12.
Convert 8.25% to a decimal
Answer: 0.0825
Step-by-step explanation:
8.25% to decimal is simply divide 8.25 by 100
8.25/100= 0.0825
The required solution after convert it into decimal is,
⇒ 0.0825
We have to given that,
Convert 8.25% into a decimal.
We can change it as,
⇒ 8.25%
Since, 1% = 1/100
Hence,
⇒ 8.25/100
⇒ 0.0825
Therefore, After convert it into decimal number solution is,
⇒ 0.0825
Learn more about the percent visit:
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A manufacturer of detergent claims that the contents of boxes sold weigh on average at least 20 ounces. The distribution of weight is known to be normal, with a standard deviation of 0.4 ounces. A random sample of 25 boxes yielded a sample mean weight of 19.87 ounces. Test at the 1% significance level the null hypothesis that the population mean weight is at least 20 ounces.
Answer:
[tex]z=\frac{19.87-20}{\frac{0.4}{\sqrt{25}}}=-1.625[/tex]
The p value for this case would be given by:
[tex]p_v =P(z<-1.625)=0.052[/tex]
Since the p value is higher than the significance level provided we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly less than 20 ounces.
Step-by-step explanation:
Information provided
[tex]\bar X=19.87[/tex] represent the sample mean
[tex]\sigma=0.4[/tex] represent the population deviation
[tex]n=25[/tex] sample size
[tex]\mu_o =68[/tex] represent the value that we want to test
[tex]\alpha=0.01[/tex] represent the significance level
z would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to test if the true mean is at least 20 ounces, the system of hypothesis would be:
Null hypothesis:[tex]\mu \geq 20[/tex]
Alternative hypothesis:[tex]\mu < 20[/tex]
The statistic is given by:
[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{19.87-20}{\frac{0.4}{\sqrt{25}}}=-1.625[/tex]
The p value for this case would be given by:
[tex]p_v =P(z<-1.625)=0.052[/tex]
Since the p value is higher than the significance level provided we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly less than 20 ounces.
Aspirin A bottle contains a label stating that it contains Spring Valley pills with 500 mg of vitamin C, and another bottle contains a label stating that it contains Bayer pills with 325 mg of aspirin. When testing claims about the mean contents of the pills, which would have more serious implications: rejection of the Spring Valley vitamin C claim or rejection of the Bayer aspirin claim? Is it wise to use the same significance level for hypothesis tests about the mean amount of vitamin C and the mean amount of aspirin? Rejection of the claim about______is more serious because the wrong______V dosage could cause more serious adverse reactions than a wrong______dosage. It would be wise to use a_______significance level for testing the claim about the aspirin.
Answer:
Rejection of the claim about aspirin is more serious because the wrong aspirin dosage could cause more serious adverse reactions than a wrong vitamin C dosage. It would be wise to use a greater significance level for testing the claim about the aspirin.
Step-by-step explanation:
The wrong dosage of aspirin will cause more damage than a wrong dosage of vitamin C. Then, if we perform an hypothesis test for each mean, the rejection of the claim about the aspirin content is more serious than the vitamin C content.
In the case of the aspirin, we want to minimize the Type II error (accepting a false null hypothesis). This can be achieved increasing the sample size or/and increasing the significance level. Then, a significative difference between the claimed content and the sample content will be easily detected.
Want Brainliest? Get this correct , Which rule should be applied to reflect f(x) = x^3 over the y-axis?
Answer:
B
Step-by-step explanation:
When you flip over the y-axis you the x is multiplied by -1
Which shapes can the composite figure be decomposed into? Check all that apply.
Answer:
rectangle ,triangle ,trapezoid ,octagon ..
Find the value of -1/3-(-5/12)
Find the sample space for a committee of two chosen from Alice (A), Bill (B), Carol (C), and David (D).
A. {(A, B), (C, D)}
B. {A, B, C, D}
C. {(A, B), (A, C), (A, D), (B, C), (B, D), (C, D)}
D. {(A, B), (A, D), (B, C), (C, D)}
Find the sample space if both sexes must be represented.
A. {(A, B), (A, C), (A, D), (B, C), (B, D), (C, D)}
B. {(A, B), (C, D)}
C. {(A, B), (A, D), (B, C), (C, D)}
D. {A, B, C, D}
Answer:
(a) C. {(A, B), (A, C), (A, D), (B, C), (B, D), (C, D)}
(b) C. {(A,B),(A,D),(B,C),(C,D)}
Step-by-step explanation:
Given four members eligible for selection:
Alice (A), Bill (B), Carol (C), and David (D).
The possible combinations are:
(A,B),(A,C),(A,D),(B,A),(B,C),(B,D),(C,A),(C,B),(C,D), (D,A),(D,B), (D,C)
Part A
Since the same pairs are equal i.e. (A, B)=(B , A),
The Sample space for a committee of two is:
{(A,B),(A,C),(A,D),(B,C),(B,D),(C,D)}
This is Option C.
Part B
If both genders must be represented, we remove the entries that contain the same gender from the sample space above.
A and C -Female
B and D - Male
{(A,B),(A,C),(A,D),(B,C),(B,D),(C,D)}
Therefore, the sample space if both genders are to be represented is:
{(A,B),(A,D),(B,C),(C,D)}
This is Option C.
Answer:
1. A
2. C
Not 100% sure but its my best guess
what is the slope of the line that contains the points (4 -1) and (-1,4)
Answer:
-1
Step-by-step explanation:
The slope formula when given two points is
m = ( y2-y1)/(x2-x1)
= (4 - -1)/(-1 -4)
= (4+1)/(-5)
= 5/-5
=-1
Answer:
-1
Step-by-step explanation:
Use the equation for slope.
[tex]m=\frac{y_{2}-y_{1} }{x_{2}- x_{1} }[/tex]
Plug in the given points into the equation.
[tex]m=\frac{4-(-1) }{-1- 4 }\\m=\frac{4+1 }{-5 }\\m=\frac{5}{-5 }\\m=\frac{1}{-1 }\\m=-1[/tex]
The slope is -1.
What is the area of a circle with a radius of 42 in use 3.14 for pi
The right answer is 5538.96 units^2
please see the attached picture for full solution
Hope it helps
Good luck on your assignment
Answer: 5538.96
Step-by-step explanation: 3.14× 42×42
42×42=1764
∴ 3.14×1764= 5538.96
In a random sample of A women, 65% favored stricter gun control laws. In a random sample of B men, 60% favored stricter gun control laws. Test the claim that the proportion of women favoring stricter gun control is higher than the proportion of men favoring stricter gun control. Use a significance level of C
Answer:
We conclude that the proportion of women favoring stricter gun control is smaller than or equal to the proportion of men favoring stricter gun control.
Step-by-step explanation:
The complete question is : In a random sample of 360 women, 65% favored stricter gun control laws. In a random sample of 220 men, 60% favored stricter gun control laws. Test the claim that the proportion of women favoring stricter gun control is higher than the proportion of men favoring stricter gun control. Use a significance level of 0.05.
Now, we are given that in a random sample of 360 women, 65% favored stricter gun control laws.
And in a random sample of 220 men, 60% favored stricter gun control laws.
Let [tex]p_1[/tex] = proportion of women favoring stricter gun control laws.
[tex]p_2[/tex] = proportion of men favoring stricter gun control laws.
SO, Null Hypothesis, [tex]H_0[/tex] : [tex]p_1\leq p_2[/tex] {means that the proportion of women favoring stricter gun control is smaller than or equal to the proportion of men favoring stricter gun control}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]p_1> p_2[/tex] {means that the proportion of women favoring stricter gun control is higher than the proportion of men favoring stricter gun control}
The test statistics that would be used here Two-sample z-test for proportions;
T.S. = [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex] ~ N(0,1)
where, [tex]\hat p_1[/tex] = sample proportion of women favoring stricter gun control laws = 65%
[tex]\hat p_2[/tex] = sample proportion of men favoring stricter gun control laws = 60%
[tex]n_1[/tex] = sample of women = 360
[tex]n_2[/tex] = sample of men = 220
So, the test statistics = [tex]\frac{(0.65 -0.60)-(0)}{\sqrt{\frac{0.65(1-0.65)}{360}+\frac{0.60(1-0.60)}{220} } }[/tex]
= 1.205
The value of z test statistics is 1.205.
Now, at 5% significance level, the z table gives critical value of 1.645 for right-tailed test.
Since, our test statistics is less than the critical value of z as 1.205 < 1.645, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.
Therefore, we conclude that the proportion of women favoring stricter gun control is smaller than or equal to the proportion of men favoring stricter gun control.
16. Terry has a monthly mortgage payment of $979. Her annual property taxes are
$1200, her PMI is $62/month, and her homeowner's insurance is $800 per year. How
much is deposited into Terry's escrow account each month?
Answer:
$228.67
Step-by-step explanation:
Given that:
Terry has a monthly mortgage payment of $979.
Terry's annual taxes are $1200 per year. That implies that his escrow each month require to posses 1/12 of that amount.
i.e 1/12 × 1200 = $100 per month.
For his homeowner's insurance which is $800 per year,
His escrow account each month is = 1/12 × 800 = $66.67
PMI = $62 per month.
Thus: The amount that is deposited into Terry's escrow account each month is the sum total of $100 + $ 66.67 + $62 = $228.67
Rachel is conducting a study in her cognitive psychology lab about people's ability to remember rhythms. She played
a short rhythm to 425 randomly chosen people. One minute later, she asked them to repeat it by clapping. If 121
people were able to successfully reproduce the rhythm, estimate the proportion of the population (including margin
of error) that would be able to successfully reproduce the rhythm.
Answer:
Rachel can conclude that 28% were able to successfully reproduce the rhythm plus or minus 5.6%
Step-by-step explanation:
To find the sample proportion that is able to successfully reproduce the rhythm = 121/425 = 0.2847 = p
Using this formula, we can calculate the margin of error
Margin of error = z*√{[p (1-p)] / n}
Where we assume a 95% level of confidence so that z* = 1.96. since one is not given, p = 0.28457 and n = 245.
Margin of error = 1.96 x √(0.28457 (1-0.28457)] / 245}
Margin of error = 1.96 x √[(0.28457 (0.7154)] / 245
= 1.96 x √(0.20/245)
= 1.96 x √0.000816
= 1.96 x 0.03
= 0.056.
Thus, Rachel can conclude that 28% were able to successfully reproduce the rhythm plus or minus 5.6%
a cell phone company test 95 cell phones and finds that seven of them have defects out of the 760 cell phones how many would you expect to have defects
Answer:
56
Step-by-step explanation:
simple ratio: 7/95 = x/760
first, calculate 7/95 which is 0.0736
next, multiply that by 760, which would be 56
Which of the following steps were applied to ABCD to obtain A'B'C'D?
A. shifted 2 units right and 3 units down
B. shifted 3 units right and 2 units down
C. shifted 2 units right and 4 units down
D. shifted 4 units right and 3 units down
Answer:
Option (A)
Step-by-step explanation:
In the figure attached,
Quadrilateral ABCD has been translated to get an image quadrilateral A'B'C'D'.
To get the rule by which the pre-image ABCD has been translated, we will choose a point A(1, 1) from the given pre-image.
Coordinates of point A' are (3, -2).
So the change is,
A(1, 1) → A'(3, -2)
A(1, 1) → A'[(1 + 2), (1 - 3)]
A(x, y) → A'[(x + 2), (y - 3)]
Therefore, point A has been shifted 2 units right and 3 units down.
Option (A) will be the answer.
Type the correct answer in the box. Spell all words correctly.
Which term describes the solution to a multiplication problem?
The
describes the solution to a multiplication problem.
Answer:
product is right
Step-by-step explanation:
OMG THIS QUESTION IS SO HARD WILL RATE IF U GET IT
Answer:
the answer is 290
Step-by-step explanation:
A = 2(wl + hl + hw)
Answer:
Step-by-step explanation:
This is a pretty easy one. Use the equation SA=2lw+2lh+2hw and substitute in the length, width, and height. Substitute than solve and you get 290 in^2
A padaria Beira Baixa vem perdendo dinheiro com a sua política de produção de venda do pãozinho francês. Atualmente, a cada dia é feita uma quantidade igual à procura do dia anterior. O proprietário, Sr. Joaquim, recolheu os seguintes dados:
Lucro na venda= $ 0,20 por unidade
Perda no pão não vendido = $ 0,05
(os pães não vendidos são moídos e vendidos como farinha de rosca: cada pão equivale a $0,15 de farinha de rosca)
Distribuição de frequência da demanda diária. Quantos pães devem ser fabricados diariamente para maximizar o lucro médio do Sr. Joaquim
1000 0,10
1100 0,10
1200 0,10
1300 0,15
1400 0,20
1500 0,15
1600 0,10
1700 0,05
1800 0,05
Answer:
The number of loaves to be made daily to maximize Mr. Joaquim's average profit is 1400.
O número de pães a serem feitos diariamente para maximizar o lucro médio do Sr. Joaquim é 1400.
Step-by-step explanation:
The table gives the daily demand of bread and the average profit that corresponds to each demand.
The daily demand values recorded ranged from 1000 to 1800.
And the corresponding average profit for the demands for each daily demand provided showed a steady increase from $0.10 as at a daily demand of 1000, through $0.15, then peaking at $0.20 at a daily demand of 1400.
After this point, the average profit begins to decline again as we move further away from the peak obtained at a daily demand of 1400.
Hence, it is evident that the daily demand that corresponds to the maximum average profit is 1400.
A daily demand of 1400 is where the peak average profit of $0.20 is obtained.
Any other demand lower or higher than 1400 corresponds to a departure from the peak profit obtained at that point according to the table of daily demand and average profits provided in the question.
In portugese/Em português
A tabela fornece a demanda diária de pão e o lucro médio que corresponde a cada demanda.
Os valores diários de demanda registrados variaram de 1000 a 1800.
E o lucro médio correspondente às demandas de cada demanda diária fornecida mostrou um aumento constante de US $ 0,10, com uma demanda diária de 1000, passando por US $ 0,15, atingindo um pico de US $ 0,20 com uma demanda diária de 1400.
Após esse ponto, o lucro médio começa a declinar novamente à medida que nos afastamos do pico obtido com uma demanda diária de 1400.
Portanto, é evidente que a demanda diária que corresponde ao lucro médio máximo é de 1.400.
Uma demanda diária de 1400 é onde é obtido o lucro médio máximo de US $ 0,20.
Qualquer outra demanda menor ou maior que 1400 corresponde a um afastamento do pico de lucro obtido nesse momento, de acordo com a tabela de demanda diária e lucros médios fornecidos na pergunta.
Hope this Helps!!!
Espero que isto ajude!!!
What is the quadratic formula?
Answer:
The quadratic formula is x= -b±√b²-4ac all over 2a
Step-by-step explanation:
The -b±√b²-4ac is part of the numerator of the fraction. And b²-4ac is all under the radical sign. The denominator is 2a so you divide -b±√b²-4ac by 2a to get the solutions of the quadratic function. Hope this helps!!
2 1 /4 meters by 1 7 /8
[tex](\frac{9}{4} )(\frac{15}{8} )[/tex]
[tex]\frac{135}{32}[/tex]
[tex]=4\frac{7}{32}[/tex]
What is the value of x?
Answer:
x = 30
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the opposite interior angles
100 = 70+x
Subtract 70 from each side
100-70 = 70+x-70
30 =x
Answer:
[tex]x = 30 \: \: degrees[/tex]
Step-by-step explanation:
The sum of the of the exterior angle is equal to sum of the opposite interior angles in a triangle.
[tex]70 + x = 100 \\ x = 100 - 70 \\ x = 30 \: \: \: degrees[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Are these correct? If not please help me write the correct answer.
Answer:
Mostly correct
For Q3, you are doing great, you remembered that negative numbers can happen if the exponent is an odd number.
For Q4, I think you were confused with the fractions,
4(i)
[tex](\frac{2}{3} )^{4} = (\frac{2^{4}}{3^{4}}) = (\frac{16}{81}) =0.198[/tex]
4(ii) is also wrong but I'll let you try to fix it yourself following what I given you for 4(i). You should get 1/64
Hope this helps!
Answer:
i = correct
ii = correct
iii = correct
iv = correct
4
i = 16/81 => 0.1975308642
ii= 1/64
Please answer this correctly
Answer:
h = 20
Step-by-step explanation:
These two shapes are similar, so you can set up a proportion like so:
[tex]\frac{72}{45} =\frac{32}{h}[/tex]
→Cross multiply:
[tex]\frac{72h}{1440}[/tex]
→Divide 1440 by 72:
h = 20
The square rootof which number is rational a7. b 1.96. c. 0.04. d. 13
Answer:
B and C
Step-by-step explanation:
We need to find which one of these numbers is a perfect square. We know 7 and 13 can be eliminated since they're prime numbers so they can't be perfect squares. B and C are both perfect squares so that's the answer.
Answer:
B and C
Step-by-step explanation:
7 = 7
1.96 = [tex]\frac{196}{100}[/tex]
0.04 = [tex]\frac{4}{100}[/tex]
13 = 13
Solving for Unknown Angles
Lines x and y are parallel.
Parallel lines x and y are intersected by lines s and t. At the intersection of lines x, t, and s, clockwise from top left, the angles are blank, blank, (6 x + 8) degrees, blank, (7x minus 2) degrees, blank. At the intersection of lines x and y, the angles are 106 degrees, 1, blank, blank. At the intersection of lines y and t, the angles are 2, blank, blank, blank.
Use the diagram to determine the measure of the unknown angle.
m∠1 = (6x + 8)°
m∠1 = 74°
What is the value of x?
What is the measure of ∠2?
(7x - 2)° + m∠2 = 106°
m∠2 =
°
Answer:
x=11
Step-by-step explanation:
x=11 because, 6x+8= 74, so you do 74-8=66 and 66/6= 11. so x=11,
the measure of 2 is 7(11)-2+m=106.
so you add 2 on both sides to cancel it out, and you end up with 7(11)+m=108
now you do 7(11)= 77, and you subtract from both sides and get 31.
therefore, m=31.
hope this helps!
Answer:
x=11
Step-by-step explanation:
From a group of 8 people 5 will each win $1000.How many different winning groups are possible?
Answer:
6720 ways different
Step-by-step explanation:
In this case, we must calculate the different ways using the permutation formula:
nPr = n! / (n - r)!
where n is the total number of people and r would come being the group of person that you want to put together the groups, therefore n = 8 and r = 5
replacing:
8P5 = 8! / (8 - 5)!
8P5 = 6720
That is to say that there are 6720 ways different winning groups are possible
Pentagon ABCDE is rotated 90° counterclockwise about the origin to form pentagon A'B'C'D'E'. What is the y-coordinate of point C'?
please now
Answer:
The y-coordinate of point C' is 4
Step-by-step explanation:
In the picture attached, pentagon ABCDE is shown.
Rotation 90° counterclockwise about the origin transforms point (x,y) into (-y,x).
C is located at (4, 3), then C' is located at (-3, 4)
Answer:
4
Step-by-step explanation:
Color Blindness in Men and Women The most common form of color blindness is an inability to distinguish red from green. However, this particular form of color blindness is much more common in men than in women (this is because the genes corresponding to the red and green receptors are located on the X-chromosome). Approximately of American men and of American women are red-green color-blind.1 Let and denote the events that a man or a woman is color-blind, respectively.
A) If an Americal male is selected at random, what is the probability that he is red-green color-blind?
B) If an American female is selected at random, what is the probability that she is not red-green color-blind?
C) If one man and one woman are selected at random, what is the probability that neither are red-green color-blind?D) If one man and one woman are selected at random, what is the probability that at least one of them is red-green color-blind?
Answer:
A. Probability the man is colorblind = 0.07
B. Probability the woman is not colorblind = 0.996
C. Probability neither the man or woman is colorblind = 0.926
D. Probability at least one of the woman or man is colorblind = 0.074
Note: The given question is missing some values. The question below is a sample question.
"The most common form of color blindness is an inability to distinguish red from green. However, this particular form of color blindness is much more common in men than in women (this is because the genes corresponding to the red and green receptors are located on the X-chromosomes). Approximately 7% of American men and 0.4% of American women are red-green color-blind.
(a) If an American male is selected at random, what is the probability that he is red-green colorblind?
(b) If an American female is selected at random, what is the probability that she is NOT red-green color-blind?
(c) If one man and one woman are selected at random, what is the probability that neither are
red-green color-blind?
(d) If one man and one woman are selected at random, what is the probability that at least one of them is red-green color-blind?"
Step-by-Step Explanation:
Let cbM and cbW represent the events that a man or a woman is colorblind, respectively.
(a) 7% of men are colorblind, P(CBM) = 7/100 = 0.07.
(b) 0.4% of women are colorblind = 0.4/100 = 0.004
P(not cbW) = 1 - P(cbW)
P(not cbW) = 1 - 0.004 = 0.996.
(c) Probability the woman is not colorblind, P(not cbW) = 0.996,
Probability that the man is not color- blind, P(not cbM) = 1 - 0.07 = 0.93.
The two events are independent of each other, therefore, their probabilities are multiplied together:
P(neither is colorblind) = P(not cbM) × P(not cbW)
= 0.93 × 0.996 = 0.926.
(d) Probability that at least one is colorblind is the complement of the set P (neither is colorblind).
Therefore, P(at least one is colorblind) = 1 - P (Neither is Colorblind)
= 1 - 0.926 = 0.074
Solve using the quadratic formula. Leave Irrational answers in radical form.
x2 + x - 20 = 0
The solutions are
and
Answer:
x1 = 4
x2 = -5
Step-by-step explanation:
There is a formula to solve the quadratic equations, which is:
[-b +- √ (b² - 4 ac) ] / (2a)
Quadractic equations have this look:
ax² + bx + c = 0
You need to stablish the numbers:
where a, is the number with x², b the x and c, the independent term.
x² + x - 20 = 0 For this case:
a = 1 ; b = 1 ; c = -20. We replace in the formula
[-1 +- √ (1² - 4 1 (-20)) ] / (2 .1)
(-1 + √81) / 2 = 4
(-1 - √81) / 2 = -5
Answer:
x1= 4 , x2= -5
Step-by-step explanation:
put in calculator MOD 5 3
a= 1 b= 1 c= -20
Please answer this correctly
Answer:
2198
Step-by-step explanation:
10×10×3.14=314
314×7
You plan to purchase dental insurance for your three remaining years in school. The insurance makes a​ one-time payment of ​$1200 in case of a major dental repair​ (such as an​ implant) or a​ one-time payment of ​$160 in case of a minor repair​ (such as a​ cavity). If you​ don't need dental repair over the next 3​ years, the insurance expires and you receive no payout. You estimate the chances of requiring a major repair over the next 3 years as 6​%, a minor repair as 59​% and no repair as 35​%. Complete parts a through c.
Required:
a. Why is X= payout of dental insurance a random variable?
A. The amount of the payout for major, mincr, or no dental repair varies over the next 3 years.
B. The probability of needing major, minor or no dental repair over the next 3 years is estimated.
C. The probability of needing major, minor, or no dental repair over the next 3 years varies.
D. The value of the payout depends on whether you will need major, minor, or no dental repair over the next 3 years.
b. Is X discrete or continuous? What are its possible values?
c. Give the probability distribution of X
Answer:
(a)D. The value of the payout depends on whether you will need major, minor, or no dental repair over the next 3 years.
(b)Discrete
(c) See below
Step-by-step explanation:
For a major dental repair, the insurance company pays $1200For a minor dental repair, the insurance company pays $160For no dental repair, the insurance company pays $0(a) X= payout of dental insurance a random variable
The payout of dental insurance, X is a random variable because the value of the payout depends on whether you will need major, minor, or no dental repair over the next 3 years. The correct option is D.
(b) X is a discrete variable. This is because its values are whole numbers.
The possible values are $1200, $160 and $0.
(c)
The probability of requiring a major dental repair (with payout of $1200) is 6%.The probability of requiring a minor dental repair (with payout of $160) is 59%.The probability of requiring no dental repair (with payout of $0) is 35%.Therefore, the probability distribution of X is given below:
[tex]\left|\begin{array}{c|c|c|c}--------------&---&---&---\\X$(Payout of dental insurance)&\$1200&\$160&\$0\\--------------&---&---&---\\P(X)&0.06&0.59&0.35\\--------------&---&---&---\end{array}\right|[/tex]