Respuesta :
A recent survey found that 70% of all adults over 50 wear glasses for driving. In a random sample of 10 adults over 50, the probability that at least six wear glasses is 84.97%.
There are only two conceivable outcomes for every adult beyond the age of 50. They either wear spectacles or they don't.
This means that we will answer the problem using the binomial probability distribution.
The binomial probability is the likelihood of achieving exactly x successes on n trials, where X can only have two possibilities.
P (X=x) = [tex]C_{n,x} * p^{x} * (1 - p)^{(1-x)}[/tex]
In which [tex]C_{n,x}[/tex] is the number of distinct combinations of x items from a collection of n elements, as determined by the formula below.
[tex]C_{n,x}[/tex] = [tex]\frac{n!}{x!(n-x)!}[/tex]
And p is the probability that X will occur.
Since we are given that n = 10 and p = 0.7
[tex]P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)[/tex]
= 84.97%
Hence, the answer is 84.97%.
Learn more about probablity:
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