Question

The mean height of an adult giraffe is 19 feet. Suppose that the distribution is normally distributed with standard deviation 0.9 feet. Let X be the height of a randomly selected adult giraffe. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N(19,0.9)b. What is the median giraffe height? 19 ft.c. What is the Z-score for a giraffe that is 22 foot tall? d. What is the probability that a randomly selected giraffe will be shorter than 18.9 feet tall? e. What is the probability that a randomly selected giraffe will be between 19.6 and 20.1 feet tall? f. The 70th percentile for the height of giraffes is ft.

Answer 1

[tex]\begin{gathered} \mu=19ft \\ \sigma=0.9ft \\ C) \\ X=22\text{ ft} \\ Z=? \\ Z=\frac{X-\mu}{\sigma} \\ Z=\frac{22ft-19ft}{0.9ft} \\ Z=3.3333 \\ The\text{ Z-score is 3.3333} \\ \\ D) \\ X<18.9ft \\ P(X\lt18.9)=? \\ Z=\frac{18.9ft-19ft}{0.9ft} \\ Z=-0.1111 \\ P(X\lt18.9)=P(Z<-0.1111),\text{ using the chart} \\ P(X\lt18.9)=P(Z<-0.1111)=0.4558 \\ The\text{ probability is 0.4558} \\ \\ E) \\ P(19.6