Question

11. Rabbit and Turtle were arguing about who was the fastest, so Rabbit challenged Turtle to a race. Now, Turtle was no fool. She knew that Rabbit would beat her in a land race, so she suggested that they each compete in the terrain they were accustomed to, and use relative quickness to compare the two. The land running speed of rabbits is normally distributed with a mean of 37 mph and standard deviation of 8.5 mph. The swimming speed of turtles is also normally distributed, with a mean of 11 mph and a standard deviation of 1.4 mph. Rabbit had a land speed average of 48 mph, while Turtie averaged 13 mph in the water. Decide which animal is relatively faster and provide evidence for your claim. (4pts)

Answer 1

Solution:

Given in the question

Mean of running land speed = 37

Standard deviation of running land speed = 8.5

Mean of swimming speed in water = 11

Standard deviation of running land speed = 1.4

For normal standardized test Mean = 0, and standard deviation = 1

To calculate relative faster speed we will use Z score as both speeds are normally distributed. Z score can be calcualted as

Z - Score = (X-mean)/SD

Z score for rabit land average speed of 48 = (48-37)/8.5

Z score = 11/8.5 = 1.29

Z score for turtle water speed of 13 = (13-11)/1.4 = 2/1.4 = 1.43

• Here we can see that Z score for turtle in the water is more than rabit land average so turtle is relatively faster than rabit.