Question

We want to estimate the mean of a population. A random sample of subjects is selected and the sample mean is computed. What is the probability that the sample mean is within 3 units of the true mean if the standard error is 1.8?

Answer 1

$\mu = ±3 \\ P(\mu-3 < \bar{X} < \mu +3) = P(\frac{(\mu-3) -\mu}{1.8} < \frac{\bar{X} - \mu}{SE} < \frac{(\mu+3)- \mu}{1.8}) \\ = P(-1.67 < Z < 1.67) \\ = P(Z< 1.67) -P(Z < -1.67) \\ = 0.9522 -0.0478 \\ = 0.9044$