Question

The mean height of an adult giraffe is 17 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-NO b. What is the median giraffe height? c. What is the Z-score for a giraffe that is 19.5 foot tall? d. What is the probability that a randomly selected giraffe will be shorter than 16.1 feet tall? e. What is the probability that a randomly selected giraffe will be between 16.6 and 17.1 feet tall? f. The 75th percentile for the height of giraffes is

Answer 1

Answer)

As the data is normally distributed we can use standard normal z table to estimate the answers

Z = (x-mean)/s.d

Given mean = 17

S.d = 1

A)

N(17, 1)

B)

For normal distribution mean and median are same = 17

C)

Z = (19.5 - 17)/1. = 2.5

D)

P(x<16.1)

Z = (16.1 - 17)/1 = -0.9

From z table, P(z<-0.9) = 0.1841

E)

P(16.6<x<17.1) = p(x<17.1) - p(x<16.6)

P(x<17.1)

Z = 0.1

From z table, P(z<0.1) = 0.5398

P(x<16.6)

Z = -0.4

From z table, P(z<-0.4) = 0.3446

Required probability is 0.5398 - 0.3446 = 0.1952

F)

From z table, P(z<0.67) = 75%

0.67 = (x - 17)/1

X = 17.67