The owner of a fish market determined that the average weight for a rainbow trout is 3.2 kilograms with a standard deviation of 0.8 kilogram.A citation rainbow trout should be one of the top 2% in weight.Assuming the weights of rainbow trout are normally distributed,at what weight (in kilograms)should the citation designation be established?
A) 4.84 kilograms.
B) 5.20 kilograms.
C) 7.36 kilograms.
D) 1.56 kilograms.

Question

Quizplus · Accepted Answer

To find the weight at which the top 2% of rainbow trout fall, we use the Z-score formula for a given percentile in a normal distribution. The Z-score for the top 2% (98th percentile) is approximately 2.05. Using the formula $Z = \frac{X - \mu}{\sigma}$, where $X$ is the weight we're solving for, $\mu = 3.2$ kg is the mean weight, and $\sigma = 0.8$ kg is the standard deviation, we rearrange to solve for $X$: $X = Z\sigma + \mu$. Plugging in the values, $X = 2.05(0.8) + 3.2 = 4.84$ kilograms.

The Owner of a Fish Market Determined That the Average