Question

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

glassesfor driving. In a random sample of 10 adults over 50, what
is theprobability that at least six wear glasses?

Answer 1

To find the probability that at least six out of ten adults over 50 wear glasses, we can use the binomial probability formula.

Step-by-step explanation:

To find the probability that at least six out of ten adults over 50 wear glasses, we can use the binomial probability formula. The probability of at least six successes can be found by summing the probabilities of getting exactly six, seven, eight, nine, or ten successes.

The formula for the binomial probability is:

`P(X=k) = C(n,k) * p^k * (1-p)^(n-k)`

Where:

• P(X=k) is the probability of getting exactly k successes
• n is the number of trials
• k is the number of successes
• p is the probability of success on a single trial

In this case, n = 10, k = 6, 7, 8, 9, 10, and p = 0.7 (probability of wearing glasses).

Answer 2

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) = (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.