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-BARSIC- [3]
1 year ago
10

10. A company finds that 45% of first-time visitors to its website do not buy any of its products. If there are 75 first-time vi

sitors on a given day, what is the probability that exactly 36 of them buy a product? Round your answer to the nearest thousandth. Answer choices: 0.044 0.080 0.450 0.550
Mathematics
1 answer:
vekshin11 year ago
8 0

Using the binomial distribution, it is found that the probability that exactly 36 of them buy a product is of 0.044.

For each first-time visitor, there are only two possible outcomes, either they buy a product, or they do not. The probability of a first-time visitor buying a product is independent of any other first-time visitor, hence the binomial distribution is used to solve this question.

<h3>What is the binomial distribution formula?</h3>

The formula is:

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

C_{n,x} = \frac{n!}{x!(n-x)!}

The parameters are:

  • x is the number of successes.
  • n is the number of trials.
  • p is the probability of a success on a single trial.

In this problem:

  • 45% of first-time visitors to its website do not buy any of its products, hence 55% buy, that is, p = 0.55.
  • There are 75 first-time visitors on a given day, hence n = 75.

The probability that exactly 36 of them buy a product is P(X = 36), hence:

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

P(X = 36) = C_{75,36}.(0.55)^{36}.(0.45)^{39} = 0.044

More can be learned about the binomial distribution at brainly.com/question/24863377

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Ashley was 98 pounds one year ago. If she now weighs 112 pounds, what is the percent increase in her weight?
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B.14.2 because you subtract the 98 to the 112
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3 years ago
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A real estate agent has 14 properties that she shows. She feels that there is a 50% chance of selling any one property during a
Ratling [72]

Answer:

91.02% probability of selling more than 4 properties in one week.

Step-by-step explanation:

For each property, there are only two possible outcomes. Either it is sold, or it is not. The chance of selling any one property is independent of selling another property. So we use the binomial probability distribution 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.

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

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

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

In this problem we have that:

n = 14, p = 0.5

Compute the probability of selling more than 4 properties in one week.

Either you sell 4 or less properties in one week, or you sell more. The sum of the probabilities of these events is decimal 1. So

P(X \leq 4)  + P(X > 4) = 1

We want to find P(X > 4). So

P(X > 4) = 1 - P(X \leq 4)

In which

P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

So

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

P(X = 0) = C_{14,0}.(0.5)^{0}.(0.5)^{14} = 0.000061

P(X = 1) = C_{14,1}.(0.5)^{1}.(0.5)^{13} = 0.000854

P(X = 2) = C_{14,2}.(0.5)^{2}.(0.5)^{12} = 0.0056

P(X = 3) = C_{14,3}.(0.5)^{3}.(0.5)^{11} = 0.0222

P(X = 4) = C_{14,4}.(0.5)^{4}.(0.5)^{10} = 0.0611

So

P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.000061 + 0.000854 + 0.0056 + 0.0222 + 0.0611 = 0.0898

Finally

P(X > 4) = 1 - P(X \leq 4) = 1 - 0.0898 = 0.9102

91.02% probability of selling more than 4 properties in one week.

8 0
3 years ago
Find the volume of a rectangular prism with a length of 2.5, a width of 8 and a height of 12
Nadya [2.5K]

Answer:

240

Step-by-step explanation:

volume of rectangular prism formula:

length*width*height

2.5*8*12=240

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3 years ago
If L | | m and m&lt;8 = 109°, what is m&lt;5
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Answer:

m∡5 = 71°

Step-by-step explanation:

m∡8 = m∡6

m∡6 + m∡5 = 180

180 - m∡6 = m∡5

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The answer is -1 7 5 hope that helped

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