Question

The mean height of an adult giraffe is 17 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.

c. What is the Z-score for a giraffe that is 18.5 foot tall?

d. What is the probability that a randomly selected giraffe will be shorter than 17.5 feet tall?

e. What is the probability that a randomly selected giraffe will be between 16.7 and 17.2 feet tall?

f. The 70th percentile for the height of giraffes is ___ ft.

Answer 1

Answer:

Median =17

Step-by-step explanation:

Given that the mean height of an adult giraffe is 17 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. X is a random variable.  

a) X is N(17, 0.9)

b) Median giraffe height = 17 ft since in normal distribution mean = median

c) When x = 18.5, Z = 18.5-17/0.9 = Z= 0.1667

d) P( x < 18) = P( Z < 56)

= 0. 2877

e) P(16.9 < x < 17.9) = P(-0.11 < z < 1) = .0.438 + 0.3413

= 0.3851

f) 75th percentile for z is 0.675

x = 17.9 + 0.9 (0.675)

= 18.5075