Respuesta :
Answer:
0.213 is the required probability.
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, 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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