The number of first-year students who will decide to live in dormitories is a binomial random variable X with n = 1000 and p = 0.50. Use the normal approximation with continuity correction to approximate the probability that X will be no more than 490, P(X $\leq$ 490).
A) 0.2743
B) 0.2709
C) 0.7291
D) 0.7357

Question

Quizplus · Accepted Answer

The normal approximation with continuity correction is given by:P(X $\leq$ 490) = P(Z $\leq$ (490 - 500) / sqrt(1000 * 0.50 * 0.50)) = P(Z $\leq$ -1) = 0.1587Using the continuity correction, we add 0.5 to the upper limit of the interval, which gives us:P(X $\leq$ 490) = P(Z $\leq$ (490.5 - 500) / sqrt(1000 * 0.50 * 0.50)) = P(Z $\leq$ -0.99) = 0.1587Therefore, the probability that X will be no more than 490 is 0.1587.

The Number of First-Year Students Who Will Decide to Live ≤\leq≤

The Number of First-Year Students Who Will Decide to Live $\leq$