**Question:** The length of sweetpea flower stems are normally distrusted with mean $\displaystyle 18.2 cm$ and standard deviation $\displaystyle 2.3 cm$. (a) Find the probability that the length of a flower stem is between $\displaystyle 16 cm$ and $\displaystyle 20 cm$. (b) $\displaystyle 12\%$ of the flower stems are longer than h cm. $\displaystyle 20\%$ of the flower stems are shorter than k cm. Find $\displaystyle h$ and $\displaystyle k$. (c) Stem lengths less than $\displaystyle 14 cm$ are unacceptable at a florist's shop. In a batch of $\displaystyle 500$ sweetpeas estimate how many would be unacceptable. **Attempt:**
$\displaystyle \mu = 18.2$ , $\displaystyle \sigma = 2.3$

$\displaystyle (a)$

█$\displaystyle P( 16 < X < 20 )$

$\displaystyle P \left( \frac{(16 -18.20}{2.3} < \frac{X - \mu}{\sigma} < \frac{(20-18.2)}{2.3} \right)$

$\displaystyle P( -0.957 < Z < 0.783)$

$\displaystyle = \phi(0.783) - ( 1 - \phi(0.8289 + 0.0018))$

$\displaystyle = 0.6139$

Answer in textbook is **0.614**
$\displaystyle (b)$

█ Don't know how to start, need help!