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.

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 19 foot tall?

d. What is the probability that a randomly selected giraffe will be shorter than 17.8 feet tall?

e. What is the probability that a randomly selected giraffe will be between 17.4 and 18.2 feet tall?

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

Answer 1

(a)

X N (17, 0.81)

X is Normal Distribution with mean = = 17 and Variance = = 0.81

(b)

Median of giraffe height = 17 ft.

(c)

X = 19

Z = (19 - 17)/0.9 = 2.2222

(d)

To find P(X<17.8):

Z = (17.8 - 17)/0.9 = 0.8889

Table of Area Under Standard Normal Curve gives area = 0.3133

So,

P(X<17.8) = 0.5 + 0.3133 = 0.8133

So,

Answer is:

0.8133

(e)

To find P(17.4<X<18.2):

Case 1: For X from mid value to 17.4:

Z = (17.4 - 17)/0.9 = 0.4444

Table of Area Under Standard Normal Curve gives area = 0.1700

Case 2: For X from mid value to 18.2:

Z = (18.2 - 17)/0.9 = 1.3333

Table of Area Under Standard Normal Curve gives area = 0.4082

So,

P(17.4<X<18.2) = 0.4082 - 0.1700 = 0.2382

So,

Answer is:

0.2382

(f)

70th percentile is given by area = 0.70 - 0.50 = 0.20 from mid value to Z on RHS.

Table gives Z = 0.525

So,

Z = 0.525 = (X - 17)/0.9

So,

X = 17 + (0.525 X 0.9)

= 17.4725

So,

Answer is:

17.4725