Answer
a) $P(x < 30,000)$ = 0.1685
b) $P(x > 34,000) \approx 0.0001$
Work Step by Step
$\mu$ =30,800, $\sigma$ = 5,600, n =45
to find probabilities when applying the central limit theorem use z = $\frac{x - \mu}{\sigma/\sqrt n}$ where $\mu$ = $\mu_{\bar{x}}$
$\mu$ = 30,800 and $\frac{\sigma}{\sqrt n}$ \approx 834.799
PART A
i) $P(x < 30,000) = P(z< \frac{30,000 - 30,800}{834.799}) \approx P(z < -0.96)$
ii) $P( z < -0.96) = 0.1685$
PART B
i) $P(x > 34,000) = P(z> \frac{34,000 - 30,800}{834.799}) \approx P(z > 3.83)$
ii) $P(z>3.83) = 1 - P(z<3.83) \approx 1-0.9999 \approx 0.0001$
