What is the probability that something with a 2.18% chance of occurring happens 3 times out of 194 events

Answer:

Line 3

Step-by-step explanation:

→ Calculate gradient

[tex]\frac{6-3}{4-2} =1.5[/tex]

Answer:

Line 3

Step-by-step explanation:

(0,0) & ( 4 , 6)

[tex]Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{6-0}{4-0}\\\\=\frac{6}{4}\\\\=\frac{3}{2}\\\\=1\frac{1}{2}[/tex]

Answer:

7 apples into 2 pieces and 4 apples into 4 pieces

Step-by-step explanation:

if you split 7 apples into 2 pieces each than you'l have 14 slices. You need 30 though which means you need 16 more. so you split 4 into 4 pieces. and the number of apples we used is 7 and 4 which make up 11. So this answer works

Answer:

Should be 5 1/2 if thats on there

Step-by-step explanation:

u take 11/2 and take out the 1 u get 10/2 so u cut 10 in half get 5 then add the one and make it 5 1/2

Answer:

B

Step-by-step explanation:

because

The probability of winning at least one prize is 0.40951.

Probability is the likelihood that an event will occur.

The following information can be deduced:

P = probability of winning = 1/10

q = probability of not winning = 1- (1/10) = 9/10

x = no. of winning

then, p (x ≥ 1) = 1 - p (x < 1)

= 1 - p (x=0)

= 1 - ⁵C₀ (1/10)^⁰ (9/10)^(5-0)

= 1 - (1) (1) (9/10)^5

=  1 - (9/10)^5

= 1 - 0.59049

= 0.40951

Therefore, the probability is 0.40951.

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sinh(ln(4)) = (exp(ln(4)) - exp(-ln(4)))/2 = (4 - 1/4)/2 = 15/8 = 1.875

sinh(4) = (exp(4) - exp(-4))/2 ≈ 27.28992

Answer:

0.0158 = 1.58% probability that all of them are under 18.

Step-by-step explanation:

Probability of independent events:

If three events, A, B and C are independent, the probability of all happening is the multiplication of the probabilities of each happening, that is:

[tex]P(A \cap B \cap C) = P(A)P(B)P(C)[/tex]

The percentage of people under the age of 18 was 23.5% in New York City, 25.8% in Chicago, and 26% in Los Angeles.

This means that [tex]P(A) = 0.235, P(B) = 0.258, P(C) = 0.26[/tex]

If one person is selected from each city, what is the probability that all of them are under 18?

Since the three people are independent:

[tex]P(A \cap B \cap C) = 0.235*0.258*0.26 = 0.0158[/tex]

0.0158 = 1.58% probability that all of them are under 18.

Answer:

0.4466 = 44.66% probability that, in exactly one of the two classes, all 8 students pass.

Step-by-step explanation:

For each student, there are only two possible outcomes. Either they pass, or they do not. The probability of an student passing is independent of other students, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Probability that all students pass in a class:

Class of 8 students, which means that [tex]n = 8[/tex]

Each student has a 95% chance of passing their class independent of the other students, which means that [tex]p = 0.95[/tex]

This probability is P(X = 8). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 8) = C_{8,8}.(0.95)^{8}.(0.05)^{0} = 0.6634[/tex]

Find the probability that, in exactly one of the two classes, all 8 students pass.

Two classes means that [tex]n = 2[/tex]

0.6634 probability all students pass in a class, which means that [tex]p = 0.6634[/tex].

This probability is P(X = 1). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{2,1}.(0.6634)^{1}.(0.3366)^{1} = 0.4466[/tex]

0.4466 = 44.66% probability that, in exactly one of the two classes, all 8 students pass.

Answer:

The cutoff time be for concert setup should be of 51.4 minutes.

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 z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Average time it takes their sound tech to set up for a show is 56.1 minutes, with a standard deviation of 6.4 minutes.

This means that [tex]\mu = 56.1, \sigma = 6.4[/tex]

If the band manager decides to include only the fastest 23% of sound techs on the tour, what should the cutoff time be for concert setup?

The cutoff time would be the 23rd percentile of times, which is X when Z has a p-value of 0.23, so X when Z = -0.74.

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

[tex]-0.74 = \frac{X - 56.1}{6.4}[/tex]

[tex]X - 56.1 = -0.74*6.4[/tex]

[tex]X = 51.4[/tex]

The cutoff time be for concert setup should be of 51.4 minutes.

Answer:

a) [tex]P(Adult)=\frac{73}{249}=0.2932=29.32%[/tex]

b) [tex]P(Chocolate)=\frac{91}{249}=0.3655=36.55%[/tex]

c) [tex]P(AdultorVanilla)=\frac{31}{83}=0.3734=37.34%[/tex]

d) [tex]P(ChildandVanilla)=\frac{10}{249}=0.0402=4.02%[/tex]

e) [tex]P(Strawberry/Child)=\frac{22}{47}=0.4681=46.81%[/tex]

f) [tex]P(Child/strawberry)=\frac{44}{95}=0.4632=46.32%[/tex]

Step-by-step explanation:

a)

In order to solve part a of the problem, we need to find the number of adults in the survey and divide them into the number of people in the survey by using the following formula>

[tex]P=\frac{desired}{possible}[/tex]

In this case we have a total of 17+43+13 adults which gives us 73 adults and a total of 249 people surveyed so we get:

[tex]P(Adults)=\frac{73}{249}=0.2932=29.32%[/tex]

b)

The same principle works for part b

there are: 40+34+17=91 people who likes chocolate ice cream the best so the probability is:

[tex]P(Chocolate)=\frac{91}{249}=0.3655=36.55%[/tex]

c)

when it comes to the or statement, we can use the following formula:

P(A or B) = P(A) + P(B) - P( A and B)

In this case:

[tex]P(Adult)=\frac{73}{249}[/tex]

[tex]P(Vanilla)=\frac{10+10+43}{249}=\frac{63}{249}[/tex]

[tex]P(AdultandVanilla)=\frac{43}{249}[/tex]

so:

[tex]P(AdultorVanilla)=\frac{73}{249}+\frac{63}{249}-\frac{43}{249}[/tex]

[tex]P(AdultorVanilla)=\frac{31}{83}=0.3734=37.34%[/tex]

d)

Is a child and likes vanilla the best.

In the table we can see that 10 children like vanilla so the probability is:

[tex]P(ChildandVanilla)=\frac{10}{249}=0.0402=4.02%[/tex]

e)

Likes strawberry the best, GIVEN that the person is a child.

In this case we can make use of the following formula:

[tex]P(B/A)=\frac{P(AandB)}{P(A)}[/tex]

so we can get the desired probabilities. First, for the probability of the person liking strawberry the best and the person being a child, we know that 44 children like strawberry the best, so the probability is:

[tex]P(childrenandstrawberry)=\frac{44}{249}[/tex]

Then, we know there are 40+10+44=94 children, so the probability for the person being a child is:

[tex]P(Child)=\frac{94}{249}[/tex]

Therefore:

[tex]P(Strawberry/Child)=\frac{\frac{44}{249}}{\frac{94}{249}}[/tex]

[tex]P(Strawberry/Child)=\frac{22}{47}=0.4681=46.81%[/tex]

f)

The same works for the probability of the person being a child given that the person likes strawberry the best.

First, for the probability of the person liking strawberry the best and the person being a child, we know that 44 children like strawberry the best, so the probability is:

[tex]P(childrenandstrawberry)=\frac{44}{249}[/tex]

Then, we know there are 44+38+13 persons like strawberry, so the probability for the person liking strawberry is:

[tex]P(Child)=\frac{95}{249}[/tex]

Therefore:

[tex]P(Child/Strawberry)=\frac{\frac{44}{249}}{\frac{95}{249}}[/tex]

[tex]P(Child/strawberry)=\frac{44}{95}=0.4632=46.32%[/tex]

Answer:

y = x + 6

Step-by-step explanation:

rise = 1

run = 1

slope = rise/run = 1

y-intercept = 6

y = mx + b

y = x + 6

Answer:

A. -¾ + 0 = -¾

B. -¾ - ¾ = -(¾ + ¾)

C. ¾ - ¾ = ¾ + (-¾)

E. -¾ + ¾ = ¾ + (-¾)

F. -¾ + ¾ = 0

Step-by-step explanation:

Let's check each equation to determine whether they are true or false.

If what we have in the both sides are equal, then the equation is true, if they're not, them it is false.

✔️-¾ + 0 = -¾

Add everything on your left together

-¾ = -¾ (TRUE)

✔️-¾ - ¾ = -(¾ + ¾)

Add everything on both sides together respectively

(-3 - 3)/4 = -(3 + 3)/4

-6/4 = -6/4 (TRUE)

✔️¾ - ¾ = ¾ + (-¾)

0 = ¾ - ¾ (+ × - = -)

0 = 0 (TRUE)

✔️-¾ + ¾ = ¾ - (-¾)

0 = ¾ + ¾ (- × - = +)

0 = 6/4 (FALSE)

✔️-¾ + ¾ = ¾ + (-¾)

0 = ¾ - ¾ (+ × - = -)

0 = 0 (TRUE)

✔️-¾ + ¾ = 0

0 = 0 (TRUE)

Answer:

0.8389 = 83.89% probability that the sample mean would be less than 133.5 liters.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

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 z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The mean per capita consumption of milk per year is 131 liters with a variance of 841.

This means that [tex]\mu = 131, \sigma = \sqrt{841} = 29[/tex]

Sample of 132 people

This means that [tex]n = 132, s = \frac{29}{\sqrt{132}}[/tex]

What is the probability that the sample mean would be less than 133.5 liters?

This is the p-value of Z when X = 133.5. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{133.5 - 131}{\frac{29}{\sqrt{132}}}[/tex]

[tex]Z = 0.99[/tex]

[tex]Z = 0.99[/tex] has a p-value of 0.8389

0.8389 = 83.89% probability that the sample mean would be less than 133.5 liters.

Answer:

12x2 – 75 = 3 (2x+5)(2x – 5)

Step-by-step explanation:

Answer:

0.758

explaination

using poisson distribution

0.08208+0.2052+0.2565+0.2138

0 .758

Answer:

5/9

Step-by-step explanation:

What we have in this question are four white balls and 5 red balls.

This is the sample space

[(4w,0R) (4w,1R)(4w,2R)(4w,3R)(4w,4R)(0w,5R)(1w,5R)(2w,5R)

So we have 9 possible sets of events

The event number with the last ball being white = 5

Probability of the last ball drawn being white = 5/9

= 0.56

Answer:

Cuboid = width*height*length

Cuboid = 24 cm^2

Answer:

The z-score for this data is Z = -0.26.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

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 z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

This is based on knowledge that in the U.S., the mean PAL is 1.65 and the standard deviation is 0.55.

This means that [tex]\mu = 1.65, \sigma = 0.55[/tex]

A study took a random sample of 51 people who lived in low income neighborhoods and found their mean PAL to be 1.63.

This means that [tex]n = 51, X = 1.63[/tex]

Using a one-sample z test, what is the z-score for this data

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

By the Central Limit Theorem

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

[tex]Z = \frac{1.63 - 1.65}{\frac{0.55}{\sqrt{51}}}[/tex]

[tex]Z = -0.26[/tex]

The z-score for this data is Z = -0.26.

Answer:

A

Step-by-step explanation:

edge 2021

Answer:

You're correct

Step-by-step explanation:

Answer:

multiplication by -1 will reflect over the x-axis

multiplication by a positive number will "scale" or "stretch" the function

Step-by-step explanation:

Step-by-step explanation:

Given that,

The mass of a patient = 70 kg

A 70kg patient has approximately 8 pints of blood.

The patient donates 470mL of blood.

We know that,

1 pint = 568 mL

8 pints = 4544 mL

Required fraction,

[tex]\dfrac{470}{4544}=0.1\\\\=\dfrac{1}{10}[/tex]

So, the required fraction is approximately [tex]\dfrac{1}{10}[/tex].

Answer: Is reinforced with other material

Step-by-step explanation:

The options are:

A is expensive to build.

B usually cracks under heavy weights.

C looks like any other road.

D is reinforced with other material.

The passage best supports the statement that a concrete road are reinforced with other material. According to the information given in the passage, steel plays a vital role in keeping the road surface flat.

Steel bars are embedded in concrete so that the stresses cannot crack the slab. Therefore, it indicates that concrete road is reinforced with other material.

Answer:

RM 1200 kalau ada gambar cuba insert

Answer: just had this problem! X = 11

You'll need 2 more lines to complete this two column proof.

---------------------

Line 4

For the "statement" portion, you'll say something like [tex]\angle 2 \cong \angle 3[/tex]

The reason for this statement is "transitive property"

We're basically combining lines 1 and 3 to form this new line.

The transitive property is the idea that if A = B and B = C, then A = C. We connect the statements like a chain.

---------------------

Line 5

The statement is what you want to prove since this is the last line.

So the statement is [tex]p || q[/tex]

The reason is "converse of corresponding angles theorem"

As you can probably guess, this theorem says "If two corresponding angles are congruent, then the lines are parallel".

Answer:

15.000 is cost so relate it with 265..hope it is help u.

Answer:

Median: 7.5

Mean: 8.6

Step-by-step explanation:

Median = the average of the 2 middle numbers of the set in ascending order, 6, 6, 6, 7, 8, 10, 12, 14

(7+8)/2 = 2

Mean = the sum of the numbers divided by the number of values

6 + 6+ 6+ 7 +8 +10 +12 +14/8

69/8

8.625

Answer:

2000

Step-by-step explanation:

2225 to the nearest 100 is 2300 but 3

<5 so it is 2000