Question

of all 3-to 5-year- old children, 56% are enrolled in school. If a sample of 500 such children is randomly selected, find the probability that at least 250 will be enrolled in school.

Answer 1

Find mean and standard deviation. Use z-scores to find z, then a z-table to find your probability based on the z-score. This is a normal approximation to the binomial distribution.

I'll get you started:

mean = np = (500)(.56) = ?
standard deviation = √npq = √(500)(.56)(.44) = ?
Note: q = 1 - p

Finish the calculations.
To find z-score:
z = (x - mean)/sd
Note: x = 250

Once you have the z-score, look in a z-table using the score to find your probability. Remember that the question is asking "at least 250" when looking at the table.

Answer 2

.243