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The 7 Humboldt penguins at the Green Valley Aquarium are very playful, and visitors love to watch them. The penguins' weights range from 8.5 to 12.5 pounds. Their mean weight is about 10.4 pounds, and the mean absolute deviation is about 1.2 pounds.
What can you conclude from these data and statistics? Select all that apply.
(A) All of the penguins weigh less than 13 pounds.
(B) The weight of the penguins typically varies by about 10.4 pounds.
(C) None of the penguins weigh less than 8.5 pounds.

The $7$ Humboldt penguins at the Green Valley Aquarium are very playful, and visitors love to watch them. The penguins' weights range from $8$ . $5$ to $12$ . $5$ pounds. Their mean weight is about $10$ . $4$ pounds, and the mean absolute deviation is about $1$ . $2$ pounds. $\newline$ What can you conclude from these data and statistics? Select all that apply. $\newline$ (A) All of the penguins weigh less than $13$ pounds. $\newline$ (B) The weight of the penguins typically varies by about $10$ . $4$ pounds. $\newline$ (C) None of the penguins weigh less than $8$ . $5$ pounds.

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Interpret confidence intervals for population means

Full solution

Q. The

7

Humboldt penguins at the Green Valley Aquarium are very playful, and visitors love to watch them. The penguins' weights range from

8

.

5

to

12

.

5

pounds. Their mean weight is about

10

.

4

pounds, and the mean absolute deviation is about

1

.

2

pounds.

\newline

What can you conclude from these data and statistics? Select all that apply.

\newline

(A) All of the penguins weigh less than

13

pounds.

\newline

(B) The weight of the penguins typically varies by about

10

.

4

pounds.

\newline

(C) None of the penguins weigh less than

8

.

5

pounds.

Penguins' Weights Range: The data provided states that the penguins' weights range from $8.5$ to $12.5$ pounds. This means that the lightest penguin weighs $8.5$ pounds and the heaviest weighs $12.5$ pounds.
Mean Weight: The mean weight of the penguins is given as $10.4$ pounds. This is the average weight of the penguins.
Mean Absolute Deviation: The mean absolute deviation (MAD) is given as $1.2$ pounds. This is the average distance between each data point (penguin's weight) and the mean (average weight).
Variability from Mean: Using the mean weight and the mean absolute deviation, we can conclude that the weights of the penguins typically vary by about $1.2$ pounds from the mean weight of $10.4$ pounds, not by $10.4$ pounds as one of the statements suggests.
Weight Range Confirmation: Since the range of weights is from $8.5$ to $12.5$ pounds, it is true that all of the penguins weigh less than $13$ pounds.
Minimum Weight: It is also true that none of the penguins weigh less than $8.5$ pounds, as this is the minimum weight in the range provided.

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