Question

the mean height of an adult giraffe is 18 feet. suppose that the distribution is normally distributed with standard deviation 0.8 feet. a. what is the z - score for a 20 foot giraffe? select b. what is the probability that a randomly selected giraffe will be shorter than 17 feet tall? select

Explanation:

Step1: Calculate z-score for 20ft giraffe

The z-score formula is $z = \frac{x - \mu}{\sigma}$, where $x=20$, $\mu=18$, $\sigma=0.8$.
$z = \frac{20 - 18}{0.8} = \frac{2}{0.8} = 2.5$

Step2: Calculate z-score for 17ft giraffe

Use the same z-score formula, where $x=17$, $\mu=18$, $\sigma=0.8$.
$z = \frac{17 - 18}{0.8} = \frac{-1}{0.8} = -1.25$

Step3: Find probability for z=-1.25

Look up $z=-1.25$ in the standard normal distribution table, which gives the cumulative probability $P(Z < -1.25) = 0.1056$

Answer:

A. 2.5
B. 0.1056