Answer
$P(\bar{x} > 551) = 0.0351$
It is unusual for the mean to be greater than 551
Work Step by Step
n = 45
$\sigma$ = 3.7
$\mu$ =550
Want to find P($\bar{x}$ > 551)
i) Find the z score corresponding to 551:
z = $\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt n}}$
z = $\frac{551 - 550}{\frac{3.7}{\sqrt 45}}$
z = 1.81
ii) $P( z > 1.81) = 1 - P( z < 1.81)$
= 1 - 0.9649
= 0.0351
iii) Therefore $P(\bar{x} > 551) = 0.0351$
It is unusual for the mean to be greater than 551. We can infer this because $P(\bar{x} > 551)$ is less than 5%.
