Question

The 10 fastest mammals on Earth have an average speed of 86.08 kilometers per hour, with a standard deviation of 13.41 kilometers per hour. The cheetah and the pronghorn have speeds of 120.7 kilometers per hour and 88.5 kilometers per hour, respectively. The lion and the jackrabbit have z-scores of −0.42 and −1.05, respectively.

Part A: List these four mammals in order from fastest to slowest.


Part B: Explain your reasoning mathematically and be sure to include all necessary calculations.

Answer 1

Cheetah (2.58), pronghorn (.18), lion (-.42), & jackrabbit (-1.05)

Step-by-step explanation:

Find the z-score of the cheetah and pronghorn using the formula: z-score = (x - mean)/standard deviation

Cheetah

z = (120.7 - 86.08)/13.41

z = 2.58

Pronghorn

z = (88.5 - 86.08)/13.41

z = .18

Answer 2

Cheetah: 120.70 km/h

Pronghorn : 88.50 km/h

Lion: 80.45 km/h

Jackrabbit: 72.00 km/h

Step-by-step explanation:

First we need to find the speeds fot he lion and the jackrabbit through the z-score formula:

`z = (V - V_(avg) )/(s)`

where V is the desired speed, s is the standard deviation and V(avg) is the average speed of the 10 fastest mammals

The lion has a speed of:

`-0.42= (V_(L) - 86.08)/(13.41)\\V_(L) = 80.45 km/h`

The jackrabbit has a speed of:

`-1.05= (V_(L) - 86.08)/(13.41)\\V_(L) = 72.00 km/h`

Listing them as fastest to slowest:

Cheetah: 120.70 km/h

Pronghorn : 88.50 km/h

Lion: 80.45 km/h

Jackrabbit: 72.00 km/h