Macintosh users make up about 5% of all computer users. A computer training school that wants to attract Macintosh users mails an advertising flyer to 25,000 computer users. If the mailing list can be considered a random sample of the population, what is the chance that at least 1245 Macintosh users will receive the flyer?

To calculate the chance that at least 1245 Macintosh users will receive the flyer, we can use the binomial probability formula.

The binomial probability formula is:
P(X >= k) = 1 - P(X < k)

Where:
P(X >= k) is the probability of getting at least k successes.
P(X < k) is the probability of getting less than k successes.

In this case, the number of Macintosh users in the mailing list follows a binomial distribution, with a success probability of 5% (0.05) and a sample size of 25000.

To calculate P(X < 1245) (the probability of getting less than 1245 Macintosh users), we can use a binomial probability calculator or statistical software.

Alternatively, we can use a normal approximation to the binomial distribution if both np and n(1-p) are greater than 5. In this case, np = 25000 * 0.05 = 1250 and n(1-p) = 25000 * 0.95 = 23750, so the condition is satisfied.

To approximate the binomial probability using the normal distribution, we can calculate the z-score and use a standard normal table or calculator. The z-score is given by:
z = (X - μ) / σ

Where:
X is the number of Macintosh users (1245 in this case),
μ is the mean of the binomial distribution (np = 1250),
and σ is the standard deviation of the binomial distribution (√(np(1-p))).

Calculating the z-score:
z = (1245 - 1250) / √(1250 * 0.95)
z = -0.1581

Using a standard normal table or calculator, we can find the probability associated with this z-score. In this case, the probability P(Z < -0.1581) is approximately 0.4372.

Therefore, P(X >= 1245) = 1 - P(X < 1245) = 1 - 0.4372 = 0.5628.

So, the chance that at least 1245 Macintosh users will receive the flyer is approximately 0.5628 or 56.28%.