The owner of a fish market has an assistant who has determined that the weights of rainbow trout are normally distributed,with mean of 3.2 kilograms and standard deviation of 0.8 kilogram.
-If a sample of 25 fish yields a mean of 3.6 kilograms,what is the Z-score for this observation?
A) 1.875
B) 18.750
C) 2.500
D) 0.750

Question

Quizplus · Accepted Answer

To find the Z-score, we use the formula:

Z = (X - μ) / (σ / √n)

Where:
X = sample mean = 3.6 kg
μ = population mean = 3.2 kg
σ = population standard deviation = 0.8 kg
n = sample size = 25

Plugging in the values, we get:

Z = (3.6 - 3.2) / (0.8 / √25)
Z = 0.4 / 0.16
Z = 2.5

Therefore, the Z-score for this observation is 2.5. The answer is C.

The Owner of a Fish Market Has an Assistant Who