Question

thanks to social media, the happiest creature on earth, an always smiling australian marsupial called a quokka, has become well known. suppose that weights of quokkas can be described by a normal model with a mean of 7 pounds and a standard deviation of 1.8 pounds. a) how many standard deviations from the mean would a quokka weighing 3 pounds be? b) which would be more unusual, a quokka weighing 3 pounds or one weighing 9 pounds? a) a quokka weighing 3 pounds is standard deviation(s) the mean. (round to two decimal places as needed.)

Explanation:

Step1: Calculate z - score for 3 pounds

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value, $\mu$ is the mean and $\sigma$ is the standard deviation. Given $\mu = 7$, $\sigma=1.8$ and $x = 3$.
$z=\frac{3 - 7}{1.8}=\frac{- 4}{1.8}\approx - 2.22$

Step2: Calculate z - score for 9 pounds

Using the same z - score formula with $x = 9$, $\mu = 7$ and $\sigma=1.8$.
$z=\frac{9 - 7}{1.8}=\frac{2}{1.8}\approx1.11$
The further a value is from the mean in terms of standard deviations, the more unusual it is. Since $| - 2.22|>1.11$, a quokka weighing 3 pounds is more unusual.

Answer:

a) - 2.22
b) A quokka weighing 3 pounds is more unusual.