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(,)

b. What is the median giraffe height? ft.

c. What is the Z-score for a giraffe that is 21 foot tall?

d. What is the probability that a randomly selected giraffe will be shorter than 19.3 feet tall?

e. What is the probability that a randomly selected giraffe will be between 18 and 18.6 feet tall?

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

Answer 1

Answer:

Given that:

The mean height of an adult giraffe is 19 feet. Suppose that the distribution is normally distributed with standard deviation 0.9 feet.

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

It is N(μ, σ^2) = N(19, 0.9^2) = N(19, 0.81)

(b) What is the median giraffe height? ft.

Median = mean = 19 ft

(c) What is the Z-score for a giraffe that is 21 foot tall?

z = (x - μ)/σ = (21 - 19)/0.9

= 2/0.9

= 2.2222

(d) What is the probability that a randomly selected giraffe will be shorter than 19.3 feet tall?

z = (19.3 - 19)/0.9

= 0.3/0.9

= 0.3333

P(x < 19.3) = P(z < 0.3333)

= 0.6293

(e)  What is the probability that a randomly selected giraffe will be between 18 and 18.6 feet tall?

z1 = (18 - 19)/0.9 = -0.1111

and z2 = (18.6 - 19)/0.9 = -0.4444

P(18.3 < x < 18.9) = P(-0.1111 < z < -0.4444)

= 0.2138

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

z- score for 70th percentile is 0.525

x = μ + z σ

= 19 + 0.525* 0.9

= 19 + 0.4725

= 19.4725