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marshall27 [118]
2 years ago
3

Suppose approximately 80% of all marketing personnel are extroverts, whereas about 70% of all computer programmers are introvert

s. (Round your answers to three decimal places.) (a) At a meeting of 15 marketing personnel, what is the probability that 10 or more are extroverts?
Mathematics
1 answer:
Ksju [112]2 years ago
7 0

Answer:

Total probability = 0.939

Step-by-step explanation:

For this problem, we need to consider both probability and permutations.

Let's first calculate the probability of exactly 10 are extroverts in the meeting.

This can be achieved in the following way:

E-E-E-E-E-E-E-E-E-E-I-I-I-I-I

Here, E signifies and extrovert, while I signifies an introvert. These could be rearranged so as to create another type of a 10 - extrovert meeting. Thus lets calculate the probability for 10 extroverts in a specific order and multiply it with the different sequences the people can be picked out.

This is:

0.8^10 * 0.2^5 = 3.43 * 10^(-5)

The number of permutations for this event is: 15!/ (10! * 5!) = 3003

This is because we are dealing with similar objects, thus permutation equation stated is correct.

Total probability for 10 extroverts: 3.43 * 10^(-5) * 3003 = 0.103

Similarly, we can find out the probabilities for 11 , 12, 13, 14, and 15 extroverts.

These are:

11 extroverts: 0.1876

12 extroverts: 0.25

13 extroverts: 0.2309

14 extroverts: 0.1319

15 extroverts: 0.0352

Total Probability = above results (in bold) combined

Total Probability = 0.939

The method stated above is the basic implementation of the binomial theorem. The results are calculated the same way as using the binomial theorem does. They are explained separately in detail to make more sense.

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Suppose the time it takes a barber to complete a haircuts is uniformly distributed between 8 and 22 minutes, inclusive. Let X =
salantis [7]

Answer:

P(X>14)= 1-P(X

And replacing we got:

P(X>14)= 1- \frac{14-8}{22-8}= 0.5714

The probability that a randomly selected barber needs at least 14 minutes to complete the haircut is 0.5714

Step-by-step explanation:

We define the random variable of interest as x " time it takes a barber to complete a haircuts" and we know that the distribution for X is given by:

X \sim Unif (a= 8, b=22)

And for this case we want to find the following probability:

P(X>14)

We can find this probability using the complement rule and the cumulative distribution function given by:

P(X

Using this formula we got:

P(X>14)= 1-P(X

And replacing we got:

P(X>14)= 1- \frac{14-8}{22-8}= 0.5714

The probability that a randomly selected barber needs at least 14 minutes to complete the haircut is 0.5714

6 0
2 years ago
An observational study found that the amount of sleep an employee gets each night is associated with job performance. The correl
Elina [12.6K]

Answer:

The correct option is D.) Causation cannot be determined from an observational study.

Step-by-step explanation:

The conclusion is not correct because

D.) Causation cannot be determined from an observational study.

Causation determined from an observational study is speculative and cannot be confirmed without data from a real experiment.

6 0
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Which pair or pairs of polygons are congruent? A. 3 and 4 B. 1 and 3 C. 1, 3, and 4 D. 2, 3, and 4 E. 1, 2, 3, and 4
iogann1982 [59]

Answer:

pair 4

Step-by-step explanation:

3 0
2 years ago
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A lecture hall seats 220 people. If 99 people are in the lecture hall, what percentage of the seats are filled?
kotykmax [81]

Answer:

45%

Step-by-step explanation:

To find the percent, we write the information as part/whole:

99/220

Now we convert to a decimal by dividing:

99/220 = 99÷220 = 0.45

Lastly, multiply by 100:

0.45(100) = 45

5 0
2 years ago
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Help. Step By Step Explanation. Ron and two of his friends ate one fourth each of an eight slice pizza. Find remaining slice of
Natasha_Volkova [10]

Answer:

2 remaining slices

Step-by-step explanation:

It sounds complicated so firstly, let's break it down.

Ron and two of his friends

There are three people involved in this question.

ate one fourth each

These three people ate one fourth of the pizza each

of an eight slice pizza.

From a pizza with eight slices

Find remaining slice of the pizza ​

The main question : remaining slice of the pizza

So since there were three people and they ate one fourth of the pizza

( One fourth's \frac{1}{4} by the way )

We need to find out how much have they ate.

Simply multiply 3 with \frac{1}{4} .

3 × \frac{1}{4} = \frac{12}{4} × \frac{1}{4}

= \frac{3}{4}

And there you go! Ron and his friends ate \frac{3}{4} of the pizza.

But that's not the end.

The main question : Remaining slice of the pizza

It's an eight slice pizza, so a slice would be : \frac{1}{8}

A full eight slice pizza would be one.

So, to find the remaining slice of pizza, simply subtract \frac{3}{4} from 1.

1 -  \frac{3}{4} =  \frac{4}{4} -  \frac{3}{4}

= \frac{1}{4}

Now there's a remainding of \frac{1}{4} of the pizza.

But the question asked for remaining slices.

So, simply convert the denominator into 8!

( Just in case you don't know what's a denominator )

\frac{numerator}{denominator}

So, simply multiply the denominator by 2 to turn 4 into 8!

And also, whenever the denominator is multiplied/ divided by any number, so do the numerator.

\frac{1 times 2}{4 times 2} = \frac{2}{8}

Your answer's the numerator, 2!

So your final answer should be 2 remaining slices out of the eight sliced pizza.

<h2>HOPE THIS ANSWER HELPED :)</h2>
8 0
2 years ago
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