Question

In a school district, 57% favor a charted school for grades K to 5. A random sample of 300 are surveyed and proportion of those who favor charter school is found. Let it be X. What is the probability that less than 50% will favor the charter school? Assume central limit theorem conditions apply.

Answer 1

The proportion of those who favor the charter school in a sample of size 300 can be modeled as a normal distribution with mean µ = 0.57 and standard deviation σ = sqrt((0.57 * 0.43)/300) = 0.035.

To find the probability that less than 50% will favor the charter school, we need to standardize the sample proportion and use the standard normal distribution.

z = (X - µ) / σ
z = (0.50 - 0.57) / 0.035
z = -2.00

Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score less than -2.00 is approximately 0.0228.

Therefore, the probability that less than 50% will favor the charter school is approximately 0.0228 or 2.28%.