Question

The mean height of an adult giraffe is 18 feet. Suppose that the distribution is normally distributed with standard deviation 1 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?

c. What is the Z-score for a giraffe that is 19 foot tall? 8.5 Incorrect

d. What is the probability that a randomly selected giraffe will be shorter than 17 feet tall?

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

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

Answer 1

X be the height of a randomly selected adult giraffe.

a) X ~ N( µ = 18 , σ = 1 )

b) For normal distribution mean = median

Therefore, median giraffe height is 18 feet.

c) z =

z =

z = 1

d. What is the probability that a randomly selected giraffe will be shorter than 17 feet tall?

P( x < 17 )

=

= P( z ≤ -1 )

= 0.1587

f. The 75th percentile for the height of giraffes ?

75th percentile means 0.75 area is to the left of the 75th percentile.

So first we need to find the number 0.7500 or nearest on the positive z score table.

0.7486 is nearest number to 0.75 on the table , it lies in the row 0.6 and across column 0.07

Therfore z score corresponding to 0.75 is 0.6+0.07 = 0.67

x = (z * σ ) + µ

x = ( 0.67*1) + 18

x = 18.67

The 75th percentile for the height of giraffes is 18.67 feet.