As the saying goes, “You can't please everyone.” Studies have shown that in a largepopulation approximately 4.5% of the population will be displeased, regardless of the
situation. If a random sample of 25 people are selected from such a population, what is the
probability that at least two will be displeased?
A) 0.045
B) 0.311
C) 0.373
D) 0.627
E) 0.689

Answers

Answer 1

Answer:

The probability that at least two people will be displeased in a random sample of 25 people is approximately 0.202.

What is probability?

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

This problem can be solved using the binomialdistribution since we have a fixed number of trials (selecting 25 people) and each trial has two possible outcomes (displeased or not displeased).

Let p be the probability of an individual being displeased, which is given as 0.045 (or 4.5% as a decimal).

Then, the probability of an individual not being displeased is:

1 - p = 0.955.

Let X be the number of displeasedpeople in a random sample of 25.

We want to find the probability that at least two people are displeased, which can be expressed as:

P(X ≥ 2) = 1 - P(X < 2)

To calculate P(X < 2), we can use the binomial distribution formula:

$P(X = k) = (^n C_k) * p^k * (1 - p)^(n-k)$

where n is the samplesize (25), k is the number of displeasedpeople, and (n choose k) is the binomial coefficient which represents the number of ways to choose k items from a set of n items.

For k = 0, we have:

$P(X = 0) = (^(25)C_ 0) * 0.045^0 * 0.955^(25)$

≈ 0.378

For k = 1, we have:

$P(X = 1) = (^(25)C_1) * 0.045^1 * 0.955^(24)$

≈ 0.42

Therefore,

P(X < 2) = P(X = 0) + P(X = 1) ≈ 0.798.

Finally, we can calculate,

P(X ≥ 2) = 1 - P(X < 2)

= 1 - 0.798

= 0.202.

Thus,

The probability that at least two people will be displeased in a random sample of 25 people is approximately 0.202.

Learn more about probability here:

brainly.com/question/14099682

#SPJ2

Answer 2

Answer:

Step-by-step explanation:

The correct answer is (B).

Let X = the number of people that are displeased in a random sample of 25 people selected from a population of which 4.5% will be displeased regardless of the situation. Then X is a binomial random variable with n = 25 and p = 0.045.

P(X ≥ 2) = 1 – P(X ≤ 1) = 1 – binomcdf(n: 25, p: 0.045, x-value: 1) = 0.311.

P(X ≥ 2) = 1 – [P(X = 0) + P(X = 1)] = 1 – 0C25(0.045)0(1 – 0.045)25 – 25C1(0.045)1(1 – 0.045)24 = 0.311.

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Answers

Answer:

Step-by-step explanation:

Working backward, $10,000 is 1% of $1,000,000, so that is the amount of the "remaining."

Apparently that is what is left of 1/2 the "remainder" after $50 million goes to the hospital. So 1/2 the "remainder" is $51M, which is also the amount the teacher gets. Those came out of a total of 2×$51M = $102M, which is the amount after the dog's $5M share.

The fortune was $107 million. The shares were ...

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Jared made 4 birds houses in 3 days how many days will it take him to make 20 bird houses

Answers

20 bird houses in 15 days.

I’m not sure but I think 12 days

In a certain online dating service, participants are given a 4-statement survey to determine their compatibility with other participants. Based on the questionnaire, each participant is notiﬁed if they are compatible with another participant. Each question is multiple choice with the possible responses of "Agree" or "Disagree," and these are assigned the numbers 1 or −1, respectively. Participant’s responses to the survey are encoded as a vector in R4, where coordinates correspond to their answers to each question. Here are the questions:

Answers

The question is incomplete. Here is the complete question.

In a certain online dating service, participants are given a 4-statement survey to determine their compatibility with other participants. Based on the questionnaire, each particpant is notified if they are compatible with another participant. Each question is multiple choice with the possible responses of "Agree" or "Disagree", and these are assigned the numbers 1 or -1, respectively. pArticipnat's responses to the survey are encoded as a vector in R4, where coordinates coreespond to their answers to each question. Here are the questions:

Question #1: I prefer outdoor activities, rather than indoor activities.

Question #2: I prefer going out to eat in restaurants, rahter than cooking at home.

Question #3: I prefer texting, rather than talking on the phone.

Question #4: I prefer living in a small town, rather than in a big city.

Here are the results for the questionaire, with a group of 5 participants:

Question1 Question2 Question3 Question4

participant A 1 1 -1 -1

participant B -1 1 1 1

participant C -1 -1 1 1

participant D 1 -1 -1 -1

participant E 1 -1 1 1

Two participants are considered to be "compatible" with each other if the angle between their compatibility vectors is 60° or less. Participants are considered to be "incompatible" if the angle between their compatibility vectors is 120° or larger. For angles between 60° or 120°, pairs of participants are warned that they "may or may not be compatible".

(a) Which pairs of paricipants are compatible?

(b) Which pairs of participants are incompatible?

(c) How would this method of testing compatibility change if the questionnaire also allowed the answer "Neutral", which would correspond to the number zero in a participant's vector? Would this be better than only

allowing "Agree" or "Disagree"? Could anything go wrong if we allowed "Neutral" as an answer?

Answer: (a) Participants A and D; B and C; C and E.

(b) Participants A and B; A and C; A and E; B and D; C and D;

Step-by-step explanation: Vectors in R4 are vectors in a 4 dimensional space and are determined by 4 numbers.

Vectors form angles between themselves and can be found by the following formula:

cos α = $(A.B)/(||A||.||B||)$

which means that the cosine of the angle between two vectors is equal the dot product of these vectors divided by the product of their magnitude.

For the compatibility test, find the angle between vectors:

1) The vectors magnitude:

Magnitude of a vector is given by:

||x|| = $\sqrt{x_(i)^(2) + x_(j)^(2)}$

Since all the vectors have value 1, they have the same magnitude:

||A|| = $\sqrt{1^(2) + 1^(2) + (-1)^(2) + (-1)^(2)}$ = 2

||A|| = ||B|| = ||C|| = ||D|| = ||E|| = 2

2) The dot product of vectors:

A·B = 1(-1) + 1(1) + (-1)1 + (-1)1 = -2

cos $\alpha_(1)$ = $(-2)/(4)$ = $(-1)/(2)$

The angle that has cosine equal -1/2 is 120°, so incompatible

A·C = 1(-1) + 1(-1) + (-1)1 + (-1)1 = -4

cos $\alpha _(2)$ = -1

Angle = 180° --------> incompatible

A·D = 1(1) + 1(-1) + (-1)(-1) + (-1)(-1) = 2

cos $\alpha _(3)$ = 1/2

Angle = 60° ---------> COMPATIBLE

A·E = 1.1 + 1(-1) + (-1)1 + (-1)1 = -2

cos $\alpha_(4)$ = -1/2

Angle = 120° --------> incompatible

B·C = (-1)(-1) + 1(-1) + 1.1 + 1.1 = 2

cos $\alpha _(5)$ = 1/2

Angle = 60° -------------> COMPATIBLE

B·D = (-1)1 + 1(-1) + 1(-1) + 1(-1) = -4

cos $\alpha_(6)$ = -1

Angle = 180° -----------> incompatible

B·E = (-1)1 + 1(-1) + 1.1 + 1.1 = 0

cos $\alpha _(7)$ = 0

Angle = 90° -------------> may or may not

C·D = (-1)1 + (-1)(-1) + 1(-1) + 1(-1) = -2

cos $\alpha_(8) =$ -1/2

Angle = 120° ---------------> Incompatible

C·E = (-1)1 + (-1)(-1) + 1.1 + 1.1 = 2

cos $\alpha_(9)$ = 1/2

Angle = 60° ---------------> COMPATIBLE

D·E = 1.1 + (-1)(-1) + (-1)1 + (-1)1 = 0

cos $\alpha_(10)$ = 0

Angle = 90° -----------------> may or may not

(c) Adding zero (0) as a component of the vectors would have to change the method of compatibility because, to determine the angle, it is necessary to calculate the magnitude of a vector and if it is a zero vector, the magnitude is zero and there is no division by zero. So, unless the service change the method, adding zero is not a good option.

There are 11 students in your class. In how many ways a group of 4 students will beselected to participate in a social campaign such that you will always be included in
the group to lead the event?

Answers

Answer:

Step-by-step explanation:

If you are always included to lead, that leaves 10 students to choose from.

If all that is important is being selected, then there are 10C3 = 120 ways to choose them.

If each selection has a unique duty, then there are 10P3 = 720 ways to assign them their jobs.

Answer: 10P3=720

Step-by-step explanation:

Is it true that Confidence intervals are always close to their true population values?

Answers

Answer:

This means that there is a 95% probability that the confidence interval will contain the true population mean. Thus, P( [sample mean] - margin of error < μ < [sample mean] + margin of error) = 0.95.

Use the number 7.14 to respond to the following:Identify the whole number.

What is the farthest place value to the right?

Write the decimal in word form.

Write the decimal in expanded form.