Question

The penguins currently living on an island are of two types, Chinstrap penguins and Gentoo penguins. The range of the heights of the Chinstrap penguins on the island is 13.2 centimeters, and the range of the heights of the Gentoo penguins on the island is 15.4 centimeters.

Which of the following statements individually provide(s) sufficient additional information to determine the range of the heights of all the penguins on the island?

Indicate all such statements.

A The tallest Gentoo penguin on the island is 5.8 centimeters taller than the tallest Chinstrap penguin on the island.
B The median height of the Gentoo penguins on the island is 1.1 centimeters greater than the median height of the Chinstrap penguins on the island.
C The average (arithmetic mean) height of the Gentoo penguins on the island is 4.6 centimeters greater than the average height of the Chinstrap penguins on the island.

Answer 1

The answer is "Option A"

Explanation:

Using the range difference to calculate the maximum and minimum value.

The range of the chinstrap penguins are:

`R(c) = Max(c) - Min(c) = 13.2`

The range of the Gentoo penguins are:

`R(g) = Max(g) - Min(g) = 15.4`

For point A:

`Max(c) = x\\\\Max(g) = x + 5.8\\\\R(c) = x - Min(c) = 13.2 \to x = 13.2 + Min(c)\\\\R(g) = x + 5.8 - Min(g) = 15.4 \to x = 9.6 + Min(g)`

equate both of them

`13.2 + Min(c) = 9.6 + Min(g)Min(g) - Min(c) = 3.6`

It indicates that Min(c) surpasses Min(g), whereas Max(g) exceeds Max (c).

Therefore, the Max is picked for g for all penguins and the minimum is picked for c.

Range of all penguins
`= Max(g) - Min(c) = x + 5.8 - x + 13.2 = 19`

Therefore, it will be determined as the option.

For point B:

In estimating the range the median height cannot help.

For point C:

In order to calculate the variety, the connection between both the mean height cannot be sued.