Question

A recent survey found that 70% of all adults over 50 wear

Answer 1

Answer:

There is an 84.97% probability that at least six wear glasses.

Step-by-step explanation:

For each adult over 50, there are only two possible outcomes. Either they wear glasses, or they do not. This means that we use the binomial probability distribution to solve this problem.

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 combinatios 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:

$n = 10, p = 0.7$

What is the probability that at least six wear glasses?

$P(X \geq 6) = P(X = 6) + `P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.8497$

There is an 84.97% probability that at least six wear glasses.