For given situation, the probability that a house belongs to the second county, knowing that it has a garage attached to it = 0.8
Assume event a: a house belongs to the first county;
event b: a house belongs to the second;
event c: a house belongs to the third;
event g: a house has an attached garage.
20% of the houses in the first county,
⇒ P(a) = 20%
30% of the houses in the second county
⇒ P(b) = 30%
50% of the houses in the first county.
⇒ P(c) = 50%
a garage is attached to 70% of the houses in the first county,
⇒ P(a ∩ g) = 70%
a garage is attached to 80% of the houses in the second county
⇒ P(b ∩ g) = 80%
and a garage is attached to 90% of the houses in the third county.
⇒ P(c ∩ g) = 90%
We need to find the probability that a house belongs to the second county, knowing that it has a garage attached to it.
i.e., P(b ∩ g) which is 80% = 0.8
Therefore, the probability that a house belongs to the second county, knowing that it has a garage attached to it is 0.8
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HELP ITS DUE TODAY!!!!!!
Answer: The second one (B)
Hope this helps! :)
Step-by-step explanation:
The times when Hayden made the bracelets in this situation don't matter. All that matters in this problem is how many he made. Since it tells you that he made them for 5 days, you would multiply the number of bracelets by the days, to get the total. (Or write the equation like so: 5*(2+4))
And of course, since they are divided into groups as the last step, we have division.
5*(2+4) /6
What is the value of 4/15 divided by -3.4
Answer:
[tex]-\frac{4}{51}\approx-0.07843[/tex]
Explanation:
[tex]\frac{4}{15}(-\frac{1}{3.4})\\\frac{4}{15}(-\frac{5}{17})\\-\frac{20}{255}\\-\frac{4}{51}\approx-0.07843[/tex]
You have a bag with five different colored marbles in it; red, green, blue, orange, and purple. Each marble has an equal chance of
being drawn from the bag and a marble is replaced after each draw.
After four draws from the bag what is the probability that you have seen both the red and green marbles at least once?
The probability that you have seen both the red and green marbles at least once is 0.3104
Given,
1/5 chance of winning a marble of any color in a drawing.
Every draw is independent and has the same probability because the marbles are replaced.
Calculating = 1- the likelihood of not receiving both red and green marbles in any of the four draws yields the same result as P, the probability of receiving both red and green marbles at least once (Q).
The union of the following three examples represents ways to not receive both red and green in all four draws:
(1)
Probability of no red and no green in a draw = 3/5.
Probability of no red and no green in 4 draws,
Q1 = 3/5 * 3/5 * 3/5* 3/5 = 81/54
The probabilities are multiplied as each draw is independent and has the same probabilities.
(2)
The probability of no red and 1 green in 4 draws is given by binomial probability.
= (4 3) (1/5)(3/5)³ = (4 * 3³)/5¹ = 108/5⁴
The probability of no red and 2 green in 4 draws is given by binomial probability.
= (4 2) (1/5)²(3/5)² == (6 * 3²)/54 = 54/5⁴
The probability of no red and 3 green in 4 draws is given by binomial probability.
= (4 3) (1/5)³(3/5) == (4 * 3)/5¹ = 12/5⁴
The probability of no red and 4 green in 4 draws is given by binomial probability.
= (4 4) = 1 * 1/5¹ = 1/5⁴⁴
Q2= sum of all 4 above probabilities.
Q2 (108 +54 + 12+1)/5 = 175/5⁴
(3)
This probability is the same as in Q2. Q3 = 175/5⁴
Therefore the probability of not seeing both red and green at all,
Q = Q1 + Q2 + Q3.
= 81 +175 + 175/5⁴ = 413/5⁴
Finally, the probability of getting both red and green at least once,
P = 1 - Q
= 1-413/5⁴
= (625 431)/625
= 194/625
= 0.3104.
The answer is 0.3104.
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A triangle has one 42° angle and two 69° angles. Is this triangle scalene?
Step-by-step explanation:
It is not a scalene triangle
because the third angle is 69⁰
Explanation: 180-(69+42)
180-111
69
You pick a card at random from an ordinary deck of 52 cards. If the card is a diamond, you get some points; if not, you lose 2 points. What value for the diamonds would make the game fair?12624 3.
Using the probability formula, the number of diamonds needed to make the game fair is determined by option (B) 6.
What is probability?Assume that there are a finite number of elementary events that are all equally likely to occur in the sample space of the experiment under consideration.
So let's say we want to determine the likelihood of an occurrence E.
So, the value of diamonds has to be:
The expected number of points that one can lose should equal the expected number of points that one can acquire for the game to be fair.
So, in order for the game to be fair, we need:
Expected points earned by selecting a diamond minus anticipated points lost by selecting a diamond.
If we choose a diamond, let's say we obtain P points.
Let X represent the random variable that records the player's score for each individual draw.
13/52 = 1/4 is the probability of selecting a diamond from a deck of 52 cards.
This is due to the fact that there are only 13 ways to choose a diamond out of the total 52 ways to choose a card.
So, the likelihood of receiving P points is 1/4, or 0.25.
The odds of not getting a diamond equal 1 minus the odds of getting a diamond equal 1 minus 0.25, which equals 0.75.
The points we receive when we don't acquire a diamond are -2. (negative since we actually lose it, so we can take it as a negative gain).
E(X) = expectation of X = 0 is therefore required (since the negative points of loosing would equate to positive point of winning, thus, making the expected overall score 0, thus, keeping it a fair game.)
We now have:
When choosing a non-diamond card, P(X = -2) equals 0.75; when choosing a diamond card, P(X = p) equals 0.25.
There are only possible values for X.
The result is:
E(X) = -2*p(X=-2)+p*p(X=p)
E(X) = -2*0.75+p*0.25
0=-1.5+0.25p
p = 1.5/0.25 = 6
Therefore, using the probability formula, the number of diamonds needed to make the game fair is determined by option (B) 6.
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Complete question:
You pick a card at random from an ordinary deck of 52 cards. If the card is a diamond, you get some points; if not, you lose 2 points. What value for the diamonds would make the game fair?
a) 12
b) 6
c) 24
d) 3
Answer:
B-6
Step-by-step explanation:
Because sample statistic is a numerical descriptive measure of a sample, every time that we randomly select observations, the sample statistics may be a different value. True False
True, the sample statistics may have a different value for each observation that is randomly chosen since they are a numerical explanatory measure of a sample.
Using sample data, a statistic is a quantitative descriptive measure. A parameter is a quantitative way to describe a population. Since whole populations (N) aren't always possible, we must rely on samples (n) as well as the statistics that can be calculated from them.
The mean, median, & mode, which are utilized at practically all math and statistics levels, are the most well-known forms of descriptive statistics. By summing together all the data set's figures & then dividing the total number of figures, the mean or average can be derived.
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Please help ASAP 100 points and the brainiest
Match the number and nature of the solutions to each equation.
1.2x2 – 6x – 8 a.one rational
2.3x2 – 5x – 3 b.two complex
3.x2 – 14x + 49 c.two irrationals
d.two rationals
what is the commission
The commission amount is $60 with the rate at 8% of earned sales amount $750.
What is the percentage?
Percentage means one part of every cent or hundred. And it is represented by symbol '%'.
Given that sales = $750 ,
and the commission rate is 8% .
Now to find the commission , we find 8% of $790
= 750 x 8 / 100
= 6000 / 100
= $60
Therefore, the commission amount is $60 with the rate at 8% of earned sales amount $750.
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Which situation represents a proportional
relationship?
The cost of purchasing boxes of paper is
$25.39 per box plus a shipping fee of
$3.25.
The cost of repairing a copy machine is
is $35.75 per hour with a service charge
of $80.50
The only option that represents a proportional relationship is;
d) The cost of repairing a computer at $54.75 per hour
How to Interpret a Proportional Relationship?Proportional relationships are defined as relationships between two variables where their ratios are equivalent.
a) The cost of purchasing boxes of paper is $25.39 per box plus a shipping fee of $3.25. If the number of boxes are x, then;
y = 25.39x + 3.25
This does not represent a proportional relationship as their ratios are not equivalent.
b) The cost of repairing a copy machine is is $35.75 per hour with a service charge of $80.50. The equation is;
y = 35.75x + 80.50
This does not represent a proportional relationship as their ratios are not equivalent.
c) The cost of purchasing printer cartridges at $34.85 per cartridge including delivery. This is not a proportional relationship as the ratio is not a straightforward one based on the delivery.
d) This represents a proportional relationship because the equation is;
y = 54.75x
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The complete options are;
a) The cost of purchasing boxes of paper for $25.39 per box plus a shipping fee of $3.25 per box .
b) The cost of repairing a copy machine at $35.75 per hour with a service charge of $80.50
c) The cost of purchasing printer cartridges at $34.85 per cartridge including delivery
d) The cost of repairing a computer at $54.75 per hour
Endure all, a manufacturer of batteries claims that the lifetime of their batteries is normally distributed with a mean of 500 hours and a standard deviation of 40 hours. What is the probability that an endure all battery selected at random will last more than 550 hours?.
Using the z-score a randomly selected Endure All battery has a 10.56% chance of lasting more than 550 hours.
What is the z-score?How closely a value relates to the mean of a set of values is measured using a Z-score.
Z-score is calculated using standard deviations from the mean.
When a data point's Z-score is 0, it indicates that its entire score is equal to the mean score.
So, how far the raw score deviates from the mean is determined using the Z score.
These steps are used to determine the Z score:
z = (x - μ)/σ
We know that: x > 550 and μ = 500, σ = 40
z = 550 - 500 / 40
z = 1.25
Using the normal distribution graph as a guide:
P(z > 1.25) = 1 - P(z < 1.25)
P(z > 1.25) = 1 - 0.8944
P(z > 1.25) = 0.1056
Therefore, using the z-score a randomly selected Endure All battery has a 10.56% chance of lasting more than 550 hours.
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Nancy ran 8 miles. How many yards did she run?
Answer: Nancy ran, 14080 yards.
Step-by-step explanation:
in how many ways can we seat 6 people at a round table if john and sam insist on sitting next to each other? (two seatings are equivalent if one is a rotation of the other.)
If John and Sam insist on sitting next to each other , then 6 people can sit at a round table in 48 ways .
In the question ,
it is given that ,
John and Sam insist to sit together ,
we have to find the number of ways , we can sit 6 people at a round table
the number of people = 6 people
there is no head of the table ,
So, first person is just a place marker so there are really only 5 people whose positions matter.
But since John and Sam are tied together, they are the equivalent of one person.
that means there are only 4 people.
= 4! × 2 ways ...because it could be (John , Sam) or (Sam, John) ,
= 48 ways .
Therefore , 6 people can sit in 48 ways .
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What Interest Rate Compounded Daily (365 Days/Year) Is Required For A $23,000 Investment To Grow To $35,500 In 6 Years?
The required Interest Rate Compounded Daily (365 Days/Year) is 7.227%.
What is compound interest?Interest on interest, or compound interest, is the adding of interest to the principle sum of a loan or deposit. It's the outcome of reinvesting interest rather than paying it out, so that interest is received on the principal plus previously collected interest in the next quarter.,
[tex]A = P(1+ \dfrac{r}{n})^{nt}[/tex]
where A is the final amount
P is the principal amount
r is the rate of interest
n is the number of times interest is charged in a year
t is the number of years
Given that interest Rate Compounded Daily (365 Days/Year) is required for a $23,000 Investment to grow To $35,500 In 6 Years. Therefore, we can write,
[tex]A = P(1+\dfrac rn)^{n \times t}[/tex]
[tex]35,500 = 23,000(1+\dfrac{r}{365})^{365 \times 6}\\\\\dfrac{35,500}{23,000} = (1+\dfrac{r}{365})^{2190}\\\\1.543478 = (1+\dfrac{r}{365})^{2190}\\\\1.000198 = 1+\dfrac{r}{365}\\\\\dfrac{r}{365} = 1.000198 - 1\\\\\dfrac{r}{365} = 0.000198[/tex]
r = 1.000198 x 365
r = 0.07227
r = 7.227%
Hence, the required Interest Rate Compounded Daily (365 Days/Year) is 7.227%.
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an ice cream cone is filled with vanilla and chocolate ice cream at a ratio of 2:1. if the diameter of the cone is 2 inches and the height is 6 inches, approximately what is the volume of vanilla ice cream in the cone? (round to nearest tenth) responses a 6.3 in3in36.3 in 3 b 2.1 in3in32.1 in 3 c 1.0 in3in31.0 in 3 d 4.2 in3
The volume of the vanilla ice cream in the cone is 4.18 cubic inches
The diameter of the cone = 2 inches
The radius of the cone = 2/1
= 1 inches
The height of the cone = 6 inches
The volume of the cone = (1/3) × π × r^2 × h
Substitute the values in the equation
= (1/3)π × 1^2 × 6
= 6.28 cubic inches
The ratio of vanilla and chocolate ice cream = 2:1
2x + x = 6.28
3x = 6.28
x = 6.28 / 3
x = 2.09
The volume of vanilla ice cream = 2x
= 2×2.09
= 4.18 cubic inches
Therefore, the volume of vanilla ice cream is 4.18 cubic inches
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Ms.D bought 8 1/2 pounds of ham from Excellente Hambaked Shop. She gave 1 3/4 pounds of ham to Mr.Chavir. How many pounds of ham does she have left?
16. john buys a cake at a bakery and a hammer at a hardware store. if there are five hardware stores and three bakeries, in how many different combinations of stores can he purchase the cake and the hammer?
15 different combinations can be used by John to buy the cake and the hammer.
Given,
John buys a cake at a bakery and a hammer at a hardware store
Number of hardware shops = 5
Number of bakeries = 3
We have to find the combinations of stores he can purchase;
Here,
5 hardware shops; H₁, H₂, H₃, H₄, H₅
3 bakeries; B₁, B₂, B₃
Now,
The combinations be like;
B₁ ; (H₁, H₂, H₃, H₄, H₅)
B₂ ; (H₁, H₂, H₃, H₄, H₅)
B₃ ; (H₁, H₂, H₃, H₄, H₅)
That is,
3 bakeries and 5 hardware shops
= 3 x 5
= 15
Therefore,
John can buy the cake and hammer in 15 different combinations.
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I'LL GIVE BRAINLIEST! PLS HELP!!!!
Todd and his friends are painting 5 equal sections of a wall. The wall is 10 feet tall, but its length is unknown. Each section will be a different color, so they need to know the area of each section.
1. Write an expression for the total area of the wall. Explain how you came up with your expression.
2. To find the area of each section, what do you need to do to the total area?
3. Write an expression for the area of each section of the wall.
1. Write an expression for the total area of the wall: 10x
2. The area of each section: 2x ft²
3. The area of each section of the wall: 2x ft²
What is area?A flat (2-D) surface's or an object's shape's overall area is known as its area. On a sheet of paper, draw a square using a pencil. It's a two-dimensional figure. The term "Area" refers to the area that a form occupies on paper.
We use cm² or m² as our units for measuring area. Area is computed by multiplying a shape's length by its breadth.
Given that,
Todd and his friends are painting 5 equal sections of a wall.
The wall is 10 feet.
1. Total area of the wall this is rectangular size wall which length is 'x' (unknown) and width/height is 10 feet.
So, area = length × height
area = 10x
2. To find the area of each section, there are 5 section (each are equal) so area of each section = total area / 5
= 10x /5
= 2x ft²
we divided total area by 5.
3. Now area of each section
= 10x/5
= 2x ft²
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For liner function f, f (2) = 0 and f (4) = -6.
Write function F in slope intercept form
How do you find the slope of the line when you have two points?
Answer:
Step-by-step explanation: y = -3x + 6
Company f sells fabrics known as fat quarters, which are rectangles of fabric created by cutting a yard of fabric into four pieces. Occasionally the manufacturing process results in a fabric defect. Let the random variable x represent the number of defects on a fat quarter created by company f. The following table shows the probability distribution of x.
By using the concept of expectation, it can be calculated that
a) Probability distribution of Y
P(Y = 0) = 0.63
P(Y = 1) = 0.25
P(Y = 2) = 0.12
b) Mean of Y = 0.49
Standard deviation of Y = 0.6999
c) Mean of selling price = $4.4
Standard deviation of selling price = $0.99
What is expectation?
At first it is important to know about probability of an event.
Probability gives us the information about how likely an event is going to occur
Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.
Probability of any event is greater than or equal to zero and less than or equal to 1.
Probability of sure event is 1 and probability of unsure event is 0.
Suppose x is a random variable with the probability function f(x). suppose
[tex]x_1, x_2, ...., x_n[/tex] are the values corrosponding to the actual occurance of the event and [tex]p_1, p_2,...., p_n[/tex] be the corrosponding probabilities.
Expectation is given by the formula
[tex]E(x) = p_1x_1 + p_2x_2 + ... + p_nx_n[/tex]
a)If a fat quarter has more than 2 defects, it cannot be sold and is discarded.
The table for the probability distribution of X is given
P(X [tex]\leq[/tex] 2) = 0.58 + 0.23 + 0.11 = 0.92
For probability distribution of Y
P(Y = 0) = P(X= 0 | X [tex]\leq[/tex] 2) = [tex]\frac{0.58}{0.92}[/tex] = 0.63
P(Y = 1) = P(X= 1 | X [tex]\leq[/tex] 2) = [tex]\frac{0.23}{0.92}[/tex] = 0.25
P(Y = 2) = P(X= 2 | X [tex]\leq[/tex] 2) = [tex]\frac{0.11}{0.92}[/tex] = 0.12
Mean of Y = 0 [tex]\times[/tex] 0.63 + 1 [tex]\times[/tex] 0,25 + 2 [tex]\times[/tex] 0.12 = 0.49
E([tex]Y^2[/tex]) = 0 [tex]\times[/tex] 0.63 + 1 [tex]\times[/tex] 0.25 + 4 [tex]\times[/tex] 0.12 = 0.73
Variance = [tex]0.73 - 0.49^2[/tex] = 0.4899
Standard deviation = [tex]\sqrt{0.4899} = 0.6999[/tex]
b) Here, E(G) = 0.40, V(G) = [tex]0.66^2[/tex]
The fat quarters sell for $5.00 each but are discounted by $1.50 for each defect found.
Selling price = 5 -1.5G
Mean of selling price = 5 - 1.5[tex]\times[/tex] 0.4 = 5 - 0.6 = $4.4
Variance of selling price = [tex]5 - 1.5^2 \times 0.66^2\\[/tex] = $0.9801
Standard deviation of selling price = [tex]\sqrt{0.9801}[/tex] = $0.99
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Complete Question
Company f sells fabrics known as fat quarters, which are rectangles of fabric created by cutting a yard of fabric into four pieces. Occasionally the manufacturing process results in a fabric defect. Let the random variable x represent the number of defects on a fat quarter created by company f. The following table shows the probability distribution of x.
x 0 1 2 3 4 or more
probability 0.58 0.23 0.11 0.05 0.03
If a fat quarter has more than 2 defects, it cannot be sold and is discarded. Let the random variable Y represent the number of defects on a fat quarter that can be sold by Company F.
(a) Construct the probability distribution of the random variable Y.
(b) Determine the mean and standard deviation of Y. Show your work.
Company G also sells fat quarters. The mean and standard deviation of the number of defects on a fat quarter that can be sold by Company G are 0.40 and 0.66, respectively. The fat quarters sell for $5.00 each but are discounted by $1.50 for each defect found.
(c) What are the mean and standard deviation of the selling price for the fat quarters sold by Company
the sales of a grocery store had an average of $8,000 per day. the store introduced several advertising campaigns in order to increase sales. to determine whether or not the advertising campaigns have been effective in increasing sales, a sample of 75 days of sales was selected. it was found that the average was $8,250 per day. from past information, it is known that the standard deviation of the population is $1,200. what is the value of the test statistic? round your answer to three decimal places.
When the standard deviation is $1200 and the mean is $8000, the test statistic's result will be -1.804.
What is test statistic?A statistic employed in statistical hypothesis testing is known as a test statistic. A test statistic, which can be thought of as a numerical summary of a data set that condenses the data into a single number that can be used to conduct the hypothesis test, is how a hypothesis test is commonly expressed. A number derived from a statistical test of a hypothesis is the test statistic. It displays how closely your actual data fit the distribution predicted by the statistical test's null hypothesis.
Here,
The claimed mean=$8250
The actual mean=$8000
The sample size=75
The standard deviation=$1200
The test statistic,
=(Actual mean-claimed mean)/Standard deviation/√(sample size)
=(8000-8250)/1200/√75
=-250/1200*1/√75
=-1.804
The value of test statistic will be -1.804 when the mean is $8000 and standard deviation is $1200.
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Of the 465 sophomores at Eastside High School, exactly 13 are taking French II or Chemistry I or both. There are 40 sophomores taking French II but not Chemistry I, and 60 sophomores taking Chemistry I but not French II. How many sophomores are taking both French II and Chemistry I ? A.
There are 55 sophomores taking French II and Chemistry I.
What is the Multiplication operation?In mathematics, Multiplication operations perform Multiplying values on either side of the operator.
For example 4×2 = 8
According to the given information, the required solution would be as:
First, we need to find the number of sophomores taking French II, Chemistry I, or both:
⇒ 1/3 × 465
Apply the multiplication operation, and we get
⇒ 155
Of the 155 sophomores, 40 are taking only French II and 60 are taking only Chemistry I:
⇒ 155 - 40 - 60
⇒ 155 - 100
Apply the subtraction operation, and we get
⇒ 55
Thus, there are 55 sophomores taking French II and Chemistry I.
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Perimeter of sector is 4 times of its radius what is the radian measurre?
The radian measures of the central angle of the sector is 2
Given,
In the question:
Perimeter of sector is 4 times of its radius .
To find the radian measures of the central angle of the sector is?
Now, According to the question:
We know:
The perimeter of the circumference is = 2[tex]\pi[/tex]r
If the perimeter of a sector is 4 times its radius.
then, the arc measure of the sector is (4r-2r) → 2r
So, if 2×[tex]\pi[/tex] radians (full circle) has a length → 2[tex]\pi[/tex]r
X radians → 2× r (the sector)
X=2× r ×(2×[tex]\pi[/tex])/(2[tex]\pi[/tex]r)
X = 2
Hence, The radian measures of the central angle of the sector is 2.
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You are going to bake an oversized sheet cake. The recipe calls for 2 cups of sugar for every 3 cups of flour. How many cups of flour are needed if you use 18 cups of sugar? Which answer is correct?
(1): 27 cups
(2): 18 cups
(3): 9 cups
(4): 6 cups
Select the equation that most accurately depicts the word problem. The perimeter of a rectangle is 68 inches. The perimeter equals twice the length of L inches, plus twice the width of 9 inches.
68 = 9L + 2
68 = L/2 + 2(9)
68 = 2/L + 2/9
68 = 9(L + 2)
68 = 2L + 2(9)
68 = 2(L - 9)
Answer:
68 = 2L + 2(9)
Step-by-step explanation:
Just write down exactly what it says!
The perimeter of a rectangle is 68 inches
68
The perimeter equals twice the length of L inches
68 = (2 × L)
Plus twice the width of 9 inches.
68 = (2 × L) + (2 × 9)
Now just clean up the equation.
68 = 2L + (2 × 9)
68 = 2L + 2(9)
The answer is 68 = 2L + 2(9).
question content area top part 1 one of the ancient stone pyramids in egypt has a square base that measures 148 m on each side. the height is 126 m. what is the volume of the pyramid?
The ancient stone pyramids in Egypt, which have a square base with a width of 148 meters and a height of 126 meters, have a volume of 9394 square metres.
What is volume?Mathematics uses cubic units to quantify volume, including cubic meters, cubic centimeters, cubic millimeters, etc. Typically, liters and gallons are used to calculate liquid volume. The loudness of a sound is measured by its volume. A container's capacity, or how much it can hold, would be determined by its volume. Cubic units established by the International System of Units are frequently used to express volume. Learn how to easily measure volume.
Here,
Side of the pyramid=148 m
Height of pyramid=126 m
Volume,
=1/2*b*h
=1/2*148*126
=9394 m²
The volume of the ancient stone pyramids in Egypt that has a square base of side 148 m and height 126m is 9394 m².
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I need help its hard pls
Patty has a photograph that is 5 inches wide and 6 inches long. She enlarged each side by the same amount. By how much was the photograph enlarged if the new area is 182 square inches? PLEASE HURRY
A stock loses 2.9 points on Monday but gains 6.4 points on Tuesday. What is the stock's overall change in points over the two days?
Answer:
3.5 Points
Step-by-step explanation:
Change means how many more points did you gain. 6.4 - 2.9= 3.5
The stocks overall change in points over the two days is 3.5 points.
Zion has scores of 92, 97, 94, and 86 on three math tests. What must his grade be on his next text so he can average test grade is a 91?
The average score is 97
What is average ?
In plain English, an average is a single number chosen to represent a group of numbers; it is often the sum of the numbers divided by the number of numbers in the group. The average of the numbers 2, 3, 4, 7, and 9 is, for instance, 5.
Average, mean, median, and norm all refer to something that sits in the middle. The average is the ratio created by dividing the total number of figures in a set by the total number of figures. scored 85 on tests on average. The term "mean" can refer to the simple average or to a value that lies halfway between two extremes.
Let the grade he got on final test be x
The average of all four grades is 91.
So, we have
(92+89+86+x)/4 = 91
⇒x=364−267
= 97
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a family decides to have children until it has three chil-dren of the same gender. assuming p(b)5p(g)5.5, what is the pmf of x5the number of children in the family?
The pmf of X = the number of children in the family is
1/4 + 3/8 + 3/8 =1
It is given that,
a family decides to have children until it has three children of the same gender i.e. BBB or GGG.
X can take the values {3,4,5}
and we know that
P(X = 3) + P(X = 4) + P(X = 5) = 1
We will find each term one by one,
P(X = 3) = ([tex]\frac{1}{2} * \frac{1}{2} * \frac{1}{2}[/tex])*2
= [tex]\frac{1}{8}[/tex] * 2
P(X = 3) = [tex]\frac{1}{4}[/tex]
P(X = 4) = ([tex]\frac{1}{2} * \frac{1}{2} * \frac{1}{2} * \frac{1}{2}[/tex])*6
= ([tex]\frac{1}{16}[/tex]) * 6
P(X =4) = [tex]\frac{3}{8}[/tex]
P(X = 5) = ([tex]\frac{1}{2} * \frac{1}{2} * \frac{1}{2} * \frac{1}{2} * \frac{1}{2}[/tex])*12
= ([tex]\frac{1}{32}[/tex])* 12
P(X = 5) = [tex]\frac{3}{8}[/tex]
Therefore the pmf equation implies,
[tex]\frac{1}{4} + \frac{3}{8} + \frac{3}{8}[/tex] = [tex]\frac{32}{32}[/tex] = 1.
The probability mass function (pmf) is also called a probbility function or frequency which characterizes the distribution of a discrete random variable. It is a function over the sample space of a discrete random variable X which gives the probability that X is equal to a certain value.
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