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julsineya [31]
4 years ago
11

The 10 fastest mammals on Earth have an average speed of 86.08 kilometers per hour, with a standard deviation of 13.41 kilometer

s 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.
Advanced Placement (AP)
1 answer:
Romashka-Z-Leto [24]4 years ago
8 0

Answer:

Cheetah: 120.70 km/h

Pronghorn : 88.50 km/h

Lion: 80.45 km/h

Jackrabbit: 72.00 km/h

Explanation:

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

z = \frac{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= \frac{V_{L} - 86.08}{13.41}\\V_{L} = 80.45 km/h

The jackrabbit has a speed of:

-1.05= \frac{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

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