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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.


a. What is the distribution of X? X ~ N([],[])


b. What is the median giraffe height? [] ft.


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 18 feet tall?[]



e. What is the probability that a randomly selected giraffe will be between 16.9 and 17.9 feet tall? []



f. The 75th percentile for the height of giraffes is [] ft.

Respuesta :

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 = [tex]\frac{18.5-17}{0.9} =0.1667[/tex]

d) [tex]P(X<18) = P(Z<0.56)\\=0.2877[/tex]

e) [tex]P(16.9<x<17.9) = P(-0.11<z<1) = 0.0438+0.3413\\=0.3851[/tex]

f) 75th percentile for z is 0.675

[tex]x=17.9+0.9(0.675)\\= 18.5075[/tex]

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