Respuesta :
Answer:
9.88% probability that fewer than 5 of them use their smartphones in meetings or classes.
Step-by-step explanation:
For each adult, there are only two possible outcomes. Either they use their smartphone is meetings or classes, or they do not. The probability of an adult using their phones is independent of other adults. 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.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
56% use them in meetings or classes.
This means that [tex]p = 0.56[/tex]
12 adult smartphone users are randomly selected
This means that [tex]n = 12[/tex]
Probability that fewer than 5 of them use their smartphones in meetings or classes.
[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{12,0}.(0.56)^{0}.(0.44)^{12} = 0.0001[/tex]
[tex]P(X = 1) = C_{12,1}.(0.56)^{1}.(0.44)^{11} = 0.0008[/tex]
[tex]P(X = 2) = C_{12,2}.(0.56)^{2}.(0.44)^{10} = 0.0056[/tex]
[tex]P(X = 3) = C_{12,3}.(0.56)^{3}.(0.44)^{9} = 0.0239[/tex]
[tex]P(X = 4) = C_{12,4}.(0.56)^{4}.(0.44)^{8} = 0.0684[/tex]
[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0001 + 0.0008 + 0.0056 + 0.0239 + 0.0684 = 0.0988[/tex]
9.88% probability that fewer than 5 of them use their smartphones in meetings or classes.
