The sample size needed to provide a margin of error of 2 or less with a .95 probability when the population standard deviation equals 11 is
A)10
B)11
C)116
D)117

Question

Quizplus · Accepted Answer

The sample size (n) can be calculated using the formula for margin of error (E) in a normal distribution: E = Z * (σ/√n), where Z is the Z-score for a 95% confidence level (approximately 1.96), σ is the population standard deviation, and E is the margin of error. Solving for n gives n = (Z * σ / E)^2. Plugging in the values: n = (1.96 * 11 / 2)^2 ≈ 116.64, which rounds up to 117.

The Sample Size Needed to Provide a Margin of Error