Question

Practice zscore question help??

The height of a sunflower is normally distributed with a mean of 14.2 feet and a standard deviation of 2.15

what is the probability of picking a sunflower that has a height greater than 16.4 feet?

Please show all work (how you found z score and final answer)

Answer 1

The $z$-score for a height of 16.4 feet is

$z=\dfrac{16.4-14.2}{2.15}\approx1.023$

So

$P(\text{height}>16.4\,\mathrm{ft})=P(Z>1.023)=1-F_Z(1.023)\approx0.153$

where $F_Z(z)=P(Z\le z)$ is the cumulative distribution function for the standard normal distribution.