Answer:
Gordo's weight = 15 pounds
It is outside the healthy weight range and is in the top 5% of weights of cats.
Gordo's weight makes Gordo unhealthy.
Step-by-step explanation:
μ = mean weight = 9.5 pounds
σ = standard deviation = 1.5 pounds
This is a normal distribution problem
We first calculate the limit of the bottom 5% of weights
Let the z-score for this limit be z'
P(z < z') = 0.05
From the normal distribution table,
z' = -1.645
And the limit for the top 5% which is z" = 1.645.
The weight that corresponds to these scores are then calculated.
Standardized scores are given as
z = (x - μ)/σ
So,
z' = (limit for the bottom 5% - μ)/σ
-1.645 = (limit for the bottom 5% - 9.5)/1.5
limit of the bottom 5% = (-1.645)(1.5) + 9.5 = 7.033 pounds
z" = ( (limit for the top 5% - μ)/σ
1.645 = (limit for the top 5% - 9.5)/1.5
limit of the bottom 5% = (1.645)(1.5) + 9.5 = 11.968 pounds
Therefore the healthy weight range for cats is (7.033 < x < 9.968)
Gordo's weight = 15 pounds
It is outside the healthy weight range and is in the top 5% of weights of cats.
Gordo's weight makes the cat unhealthy.
Flaco's weight = 8 pounds
Flaco's weight lies in the healthy weight range for cats. Hence, Flaco is a healthy cat.
