Respuesta :
Answer:
0.213 is the required probability. Â
Step-by-step explanation:
We are given the following information:
We treat person booking from online travel website as a success.
P(Booking through online travel website) = 0.68
Then the number of people follows a binomial distribution, where
[tex]P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}[/tex]
where n is the total number of observations, x is the number of success, p is the probability of success.
Now, we are given n = 15
P(exactly ten people out of fifteen people used an online travel website)
[tex]P(x = 10)\\\\= \binom{15}{10}(0.68)^{10}(1-0.68)^5 \\\\= 0.213[/tex]
0.213 is the probability that exactly ten people out of fifteen people used an online travel website when they booked their hotel.
Taking into accountthe definition of binomial distribution, Â the probability that exactly ten people out of fifteen people used an online travel website when they booked their hotel is 0.213.
It is said that a variable is discrete when it cannot take any value between two consecutive ones, that is, its events do not assume intermediate values ​​between two values.
A binomial distribution is a discrete probability distribution that describes the number of successes when conducting n independent experiments on a random variable.
In other words, the binomial distribution is a discrete probability distribution that tells the percentage that a result is likely to be obtained between two possibilities when performing n number of tests.
The probability of each possibility cannot be greater than 1 and cannot be negative.
The expression to calculate the normal distribution is:
[tex]P_{x} =[/tex]([tex]n\\ x[/tex])[tex]p^{x} q^{n-x}[/tex]
Where:
- n = Number of trials / experiments
- x = Number of successes
- p = Probability of success
- q = Probability of failure (1-p)
Remember that:
([tex]n\\ x[/tex])= [tex]\frac{n!}{x!(n-x)!}[/tex]
where the exclamation point "!" indicates the factorial of a positive integer n, which is defined as the multiplication between all the positive integers that exist between the number that appears in the formula and the number 1:
n!= n× (n-1)× (n-2)×... × 2× 1
In this  case, you know:
- n= 15
- x=10
- p=0.68
- q= 1- 0.68=0.32
Replacing
[tex]P_{10} =[/tex]([tex]15\\ 10[/tex])[tex]0.68^{10} 0.32^{15-10}[/tex]
Solving:
[tex]P_{10} =\frac{15!}{10!(15-10)!}x0.68^{10} x0.32^{15-10}[/tex]
[tex]P_{10} =3003x0.68^{10} x0.32^{5}[/tex]
[tex]P_{10} =0.213[/tex]
Finally, the probability that exactly ten people out of fifteen people used an online travel website when they booked their hotel is 0.213.
Learn more:
- https://brainly.com/question/20815137?referrer=searchResults
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