Answer
$P(x < 18) = 0.0013 $
Yes, it would be unusual for an egg to hatch in less than 18 days. This is because the probability that an egg hatches in less than 18 days is 0.0013, which is less than 0.05. Furthermore, 18 days is an unusual value because it is 3 standard deviations below the mean time it takes for an egg to hatch (as indicated by its z-score).
Work Step by Step
$\mu$ = 21, $\sigma$ = 1
Want to find $P(x< 18)$:
1) Convert 18 to a z-score:
z = $\frac{x - \mu}{\sigma}$
z = $\frac{18 - 21}{1}$
z = -3
2) $P(x < 18) = P( z < -3)$ = 0.0013
Yes, it would be unusual for an egg to hatch in less than 18 days. This is because the probability that an egg hatches in less than 18 days is 0.0013, which is less than 0.05. Furthermore, 18 days is an unusual value because it is 3 standard deviations below the mean time it takes for an egg to hatch (as indicated by its z-score).
