Suppose it is known that 60% of radio listeners at a particular college are smokers. A sample of 500 students from the college is selected at random. Approximate the probability that at least 280 of these students are radio listeners.

The probability that at least 280 of these students are smokers is 0.9664.

Step-by-step explanation:

Let the random variable X be defined as the number of students at a particular college who are smokers

The random variable X follows a Binomial distribution with parameters n = 500 and p = 0.60.

But the sample selected is too large and the probability of success is close to 0.50.

So a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:

1.np ≥ 10

2.n(1 - p) ≥ 10

Check the conditions as follows:

Thus, a Normal approximation to binomial can be applied.

So,  

Compute the probability that at least 280 of these students are smokers as follows:

Apply continuity correction:

P (X ≥ 280) = P (X > 280 + 0.50)

                   = P (X > 280.50)

*Use a z-table for the probability.

Thus, the probability that at least 280 of these students are smokers is 0.9664.

you would have to sell 24 bracelets.

step-by-step explanation:

84/3.5 = 24